ES2963344T3 - Función de formación en ventanas de análisis / síntesis para la transformada con solapamiento modulada - Google Patents

Función de formación en ventanas de análisis / síntesis para la transformada con solapamiento modulada Download PDF

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ES2963344T3
ES2963344T3 ES18796463T ES18796463T ES2963344T3 ES 2963344 T3 ES2963344 T3 ES 2963344T3 ES 18796463 T ES18796463 T ES 18796463T ES 18796463 T ES18796463 T ES 18796463T ES 2963344 T3 ES2963344 T3 ES 2963344T3
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Markus Schnell
Manfred Lutzky
Alexander Tschekalinskij
Ralf Geiger
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Abstract

Se proporcionan métodos y aparatos para realizar la transformación de coseno modificado (MDCT) con una función de ventana de análisis/síntesis, usando una función de ventana de análisis (40, 50, 60, 70, 240) que tiene una porción serpenteante (44, 64, 244) que pasa una función lineal (40', 240') en correspondencia de al menos cuatro puntos (#1, #2, #3, #4). (Traducción automática con Google Translate, sin valor legal)

Description

DESCRIPCIÓN
Función de formación en ventanas de análisis / síntesis para la transformada con solapamiento modulada
1. Antecedentes
[0001] Las transformadas con solapamiento se han desarrollado para varias aplicaciones de codificación de audio. Estas transformadas se realizan normalmente en bloques consecutivos de un conjunto de datos más grande (por ejemplo, dos tramas consecutivas) para una señal de audio. Los bloques sucesivos pueden estar solapados. Por consiguiente, una última parte de un bloque coincide con una primera parte de un bloque sucesivo. Se puede utilizar una función de formación en ventanas.
[0002] Se han desarrollado ventanas de transformada de coseno discretas modificadas (MDCT) asimétricas, de transformada de seno discretas modificadas (MDST) asimétricas, transformaciones de tiempo a frecuencia, que representan transformadas con solapamiento moduladas.
[0003] En los últimos años se han desarrollado ventanas de transformada de coseno discretas modificadas (MDCT) asimétricas, ventanas de transformada de seno discretas modificadas (MDST) asimétricas y otros tipos de ventanas, dado que proporcionan respuestas de frecuencia mejoradas en comparación con las formas simétricas, especialmente para aplicaciones de señal de bajo retraso, tales como las aplicaciones de codificación de audio.
[0004] La primera generación de formas de ventana se centró simplemente en el diseño de la respuesta de frecuencia, por ejemplo, la ventana G.718 o MPEG-4 AAC-ELD. Los recientes desarrollos también tienen en cuenta la forma temporal de la ventana que es responsable de la modulación temporal del error de cuantificación, por ejemplo, la ventana ALDO tal como se utiliza en el códec EVS de 3GPP.
[0005] Sin embargo, la estrategia de diseño presentada allí presenta el problema de que las formas de ventana muestran una diferenciación no continua que conduce a una respuesta de frecuencia sub-óptima. La invención descrita en este documento presenta una solución para superar este problema.
[0006] HENRIQUE S MALVAR, “Biorthogonal and Nonuniform Lapped Transforms for Transform Coding with Reduced Blocking and Ringing Artifacts”, IEEE TRANSACTIONS ON SIGNAL PROCESSING, IEEE SERVICE CEN-TER, NUEVA YORK, NY, EE. UU., vol. 46, no. 4, Abril de 1998, describe un procedimiento que comprende el hecho de realizar un análisis de transformada de coseno modificada, MDCT, para transformar una representación en el dominio del tiempo, TD, de una señal de información, o una versión procesada de la misma, en una representación en el dominio de la frecuencia, FD, mediante una función de formación en ventanas de análisis que presenta una parte serpenteante que pasa por una función lineal en correspondencia de al menos cuatro puntos.
[0007] “ISO/IEC 14496-3:2005/FDAM 9, AAC-ELD”, 82. MPEG MEETING; 22-10-2007 - 26-10-2007; SHEN-ZHEN; (MOTION PICTURE EXPERT GROUP OR ISO/IEC JTC1/SC29/WG11), no. N9499, 21 de Febrero de 2008 describe una técnica para ventanas de síntesis con una parte serpenteante.
[0008] El documento US 2017/011747 A1 (FAURE JULIEN [FR] Y COL.) 12 de Enero de 2017 describe una ventana de síntesis simétrica con una parte serpenteante y ventana de análisis correspondiente.
[0009] David Virette, “Low Delay Transform for High Quality Low Delay Audio Coding”, 10 de Diciembre de 2012, páginas 1-195 describe técnicas en base a transformadas avanzadas para codificación de audio de bajo retraso.
2. Resumen de la invención
[0010] La invención se define en las reivindicaciones independientes.
3. Descripción de los dibujos
[0011]
Las Figuras 1 y 2 muestran esquemas según la técnica anterior.
Las Figuras 3 a 12 muestran esquemas de funciones según los ejemplos.
Las Figuras 13 y 13A muestran codificadores según los ejemplos.
Las Figuras 14 y 14A muestran decodificadores según los ejemplos.
Las Figuras 15 y 16 muestran procedimientos según los ejemplos.
Las Figuras 17 y 18 muestran aparatos según los ejemplos.
La Figura 19 muestra un esquema según los ejemplos.
La Figura 20 muestra un esquema según la técnica anterior.
Las Figuras 21 a 25 muestran esquemas según los ejemplos.
Las Figuras 26 a 31 muestran esquemas de funciones según los ejemplos.
4. Ejemplos
[0012] Una señal de audio (denominada a continuación “señal de información”) se puede describir en el dominio de tiempo, TD, como una sucesión de muestras (por ejemplo, xb(n) para un bloque b e índice, por ejemplo, momento, n). La representación en el TD puede estar formada por una pluralidad de tramas asociadas, cada una, a una pluralidad de muestras. En el dominio de la frecuencia, FD, una trama se puede representar como una sucesión de bins (por ejemplo, X(k) asociados, cada uno, a una frecuencia particular (siendo cada frecuencia asociada a un índice k).
[0013] Es posible convertir una representación en el TD en una representación en el FD mediante una técnica de transformada con solapamiento modulada (tal como una técnica de transformada de coseno discreta modificada, MDCT, o una técnica de transformada de seno discreta modificada, MDST, por ejemplo). Tal técnica puede implementarse, por ejemplo, en el lado de un codificador, para transformar los valores muestreados en valores de frecuencia.
[0014] Es posible convertir una representación FD en una representación en el TD mediante una técnica de transformada con solapamiento modulada inversa (tal como una técnica de transformada de coseno discreta modifi cada inversa, IMDCT, o una técnica de transformada de seno discreta modificada inversa, IMDST). Tal técnica puede implementarse, por ejemplo, en un lado decodificador, para transformar los valores de frecuencia en valores de TD (por ejemplo, para realizar la reproducción).
[0015] La siguiente tabla indica los símbolos utilizados en los siguientes segmentos:
[0016] Las Figuras 13 y 13A muestran aparatos codificadores, respectivamente 130 y 130A. Cada uno de los aparatos codificadores 130 o 130A puede comprender una pluralidad de herramientas, tales como bloques funcionales capaces de realizar técnicas de procesamiento de señal. Cada uno de estos bloques puede ser un dispositivo inde pendiente o puede ser un bloque funcional que divide una estructura de hardware con otras herramientas del aparato codificador 130 y 130A.
[0017] El aparato codificador 130 o 130A comprende una herramienta de transformada con solapamiento mo dulada 131 (tal como una herramienta de transformación de coseno discreta modificada, MDCT, de bajo retraso o una herramienta de transformada de seno discreta modificada, MDST, de bajo retraso u otro tipo de herramienta de transformada con solapamiento modulada) que convierte una señal de información (por ejemplo, una señal de audio) de una representación en el dominio de tiempo, TD, en una representación en el dominio de la frecuencia, FD. La herra mienta de transformada con solapamiento modulada 131 (por ejemplo, herramienta MDCT o MDST) realiza un análisis de transformada con solapamiento modulada (por ejemplo, un análisis de MDCT, un análisis de MDST).
[0018] Otras herramientas son previstas, por ejemplo, de forma descendente a la herramienta de transformada con solapamiento modulada 131 o que funcionen en el TD. Algunas de ellas se mencionan aquí.
[0019] El aparato codificador 130 puede comprender una herramienta de codificación predictiva lineal, LPC, 132 para realizar un análisis de LPC en el FD. El aparato codificador 130A puede comprender una herramienta de configuración de ruido espectral, SNS, 132A para realizar un análisis de LPC en el FD.
[0020] SNS puede verse como una generalización de LPC y, por lo tanto, en algunos ejemplos, el bloque de LPC 132 puede verse como un ejemplo particular de la herramienta de SNS 132A (y el aparato codificador 130 puede verse como un ejemplo particular del aparato codificador 130A).
[0021] Cada uno de los aparatos codificadores 130 y 130A puede comprender una herramienta de configura ción de ruido temporal, TNS, 133, para controlar la forma temporal del ruido dentro de cada ventana de la señal de información (por ejemplo, como emitida por la herramienta de transformada con solapamiento modulada) en el FD.
[0022] Cada uno de los aparatos codificadores 130 y 130A puede comprender un cuantificador espectral 134 que procesa señales en el FD. La señal emitida por la herramienta de TNS 133 se puede cuantificar, por ejemplo, mediante cuantificación escalar de zona muerta más umbrales uniformes.
[0023] Cada uno de los aparatos codificadores 130 y 130A puede comprender un estimador del nivel de ruido 136, por ejemplo, de forma descendente al cuantificador espectral 134.
[0024] Cada uno de los aparatos codificadores 130 y 130A puede comprender un codificador 135 que procesa señales en el FD, por ejemplo, para realizar la codificación de entropía, por ejemplo, para comprimir un flujo de bits. El codificador 135 puede, por ejemplo, realizar la codificación de entropía.
[0025] Cada uno de los aparatos codificadores 130 y 130A puede comprender un detector de ancho de banda 137a que puede controlar, por ejemplo, un controlador de ancho de banda en el decodificador.
[0026] Cada uno de los aparatos codificadores 130 y 130A puede comprender herramientas que procesan señales en el dominio de tiempo, TD. Por ejemplo, el aparato codificador 130 o 130A puede comprender una herra mienta de remuestreo 138a (por ejemplo, un muestreador hacia abajo) y/o una herramienta de post-filtrado a largo plazo, LTPF, 138b, para controlar un LTPF activo en el TD en el lado del decodificador.
[0027] Cada uno de los aparatos codificadores 130 y 130A puede comprender una herramienta multiplexora de flujo de bits (redactor de flujo de bits) 137 para preparar un flujo de bits con datos obtenidos de las herramientas del TD y/o del FD colocadas de forma ascendente. El flujo de bits puede comprender una representación digital de una señal de información junto con los datos de control que se van a utilizar en el lado del decodificador. El flujo de bits puede estar comprimido o incluir partes que están comprimidas.
[0028] Las Figuras 14 y 14A muestran el aparato decodificador respectivamente 140 y 140A. Cada uno de ellos puede decodificar una representación digital de una señal de información, por ejemplo, como codificada por el codificador 130 o 130A, por ejemplo.
[0029] Cada uno de los aparatos decodificadores 140 y 140A puede comprender una herramienta de transfor mada con solapamiento modulada inversa 147 (por ejemplo, una herramienta de MDCT inversa de bajo retraso o una herramienta de DMST inversa de bajo retraso) para transformar las representaciones de señal del FD al TD. La herramienta de transformada con solapamiento modulada 147 realiza una síntesis de transformada con solapamiento mo dulada (por ejemplo, una síntesis de MDCT y/o una síntesis de MDST, etc.).
[0030] Se proporcionan otras herramientas, por ejemplo, de forma ascendente a la herramienta de transformada con solapamiento modulada inversa 147 o que funcionan en el TD. Algunas de ellas se mencionan aquí.
[0031] Cada uno de los aparatos decodificadores 140 y 140A puede comprender una herramienta múltiplex de flujo de bits 141 para obtener un flujo de bits (por ejemplo, por transmisión) de un aparato codificador (por ejemplo, el aparato 130 o 130A). Por ejemplo, se puede proporcionar una salida del aparato codificador 130 o 130A como una señal de entrada en el aparato decodificador 140 o 140A.
[0032] Cada uno de los aparatos decodificadores 140 y 140A puede comprender un decodificador 142 que puede, por ejemplo, descomprimir datos en el flujo de bits. Se puede realizar una decodificación aritmética. Se puede realizar una decodificación residual.
[0033] Cada uno de los aparatos decodificadores 140 y 140A puede comprender una herramienta de relleno de ruido 143 que procesa señales en el FD.
[0034] Cada uno de los aparatos decodificadores 140 y 140A puede comprender una herramienta de ganancia global 144 que procesa señales en el FD.
[0035] Cada uno de los aparatos decodificadores 140 y 140A puede comprender una herramienta decodifica dora TNS 145 que procesa señales en el FD.
[0036] El aparato decodificador 140 puede comprender una herramienta de conformación de MDCT (o MDST) 146 (otras herramientas de transformada con solapamiento son posibles). La herramienta de conformación de MDCT (o MDST) 146 puede procesar señales aplicando factores de ganancia calculados a partir de coeficientes de filtro de LP decodificados (obtenidos de una herramienta de decodificación LPC 146a, por ejemplo) transformados al espectro de FD (por ejemplo, espectro de MDCT o MDST, etc.).
[0037] El aparato decodificador 140A puede comprender una herramienta decodificadora de SNS 146A', por ejemplo, obteniendo coeficientes de LPC de la herramienta de SNS 132A.
[0038] Cada uno de los aparatos decodificadores 140 y 140A puede comprender una herramienta de LTPF 148 para realizar un post-filtro en el TD.
[0039] El aparato decodificador 140A puede comprender un controlador de ancho de banda de decodificador 149 que puede obtener la información de ancho de banda del detector de ancho de banda 137a, por ejemplo.
[0040] El aparato codificador 130 (o 130A) y el aparato decodificador 140 (o 140A) pueden estar compuestos entre sí para formar un sistema.
[0041] Básicamente, las herramientas de forma descendente a la herramienta de transformada con solapamiento modulada 131 en el aparato codificador 130 o 130A y las herramientas de forma ascendente a la herramienta de transformada con solapamiento modulada inversa 147 en el aparato decodificador 140 o 140A pueden realizar el procesamiento de señal en el FD y, por lo tanto, son herramientas de FD.
[0042] Las técnicas se discuten aquí con respecto a las técnicas de conversión, por ejemplo, en las herramien tas 131 y 147.
[0043] En términos generales, MDCT, MDST, etc., son transformadas discretas que presentan la propiedad adicional de ser transformadas con solapamiento. Una de estas transformadas se realiza en bloques consecutivos de un conjunto de datos más grande (por ejemplo, dos tramas consecutivas). Los bloques sucesivos se pueden solapar. Por consiguiente, una última parte de un bloque puede coincidir con una primera parte de un bloque sucesivo. Se puede utilizar una función de formación en ventanas Wn (n = 0, ..., 2N-1). En particular, la función de formación en ventanas se puede utilizar como un peso. Una ventaja es que es posible evitar o reducir las discontinuidades en los bordes de los bloques.
[0044] La Figura 15 muestra un procedimiento 150 para realizar un análisis de transformada con solapamiento modulada, por ejemplo, en la herramienta de transformada con solapamiento modulada 131 (que puede ser una herramienta de MDCT). La señal de entrada Xb(n) de la trama actual b puede constar de N muestras de audio, donde la más nueva se sitúa en Xb(N - 1).
[0045] En la etapa S151, los búferes de entrada pueden actualizarse. El búfer de entrada de tiempo para la transformada con solapamiento moduladatpuede actualizarse según:
t(n )=xb_1(Z n )paran=0..N - 1 — Z
t(N — Z n)=xb(n)para n = 0..N — 1
t(2N — Z n) = 0 para n=0..Z — 1
[0046] Este último es una inicialización que sólo se requiere por motivos de consistencia.
[0047] En la etapa S152, un bloque de N muestras de tiempo se puede transformar a coeficientes de frecuencia X(k) mediante la siguiente ecuación:
donde<wn>es una ventana de transformada con solapamiento modulada asimétrica (por ejemplo, una ventana de MDCT) según el tamaño de trama utilizado.
[0048] La Figura 16 muestra un procedimiento 160 para realizar una síntesis de transformada con solapamiento modulada (por ejemplo, síntesis de MDCT), por ejemplo, en la herramienta de transformada con solapamiento modu-X¡j(k)
lada 147 (que puede ser una herramienta de IMDCT). Aquí, un espectro (es decir, una representación en el FD) se puede transformar al TD mediante las siguientes etapas:
En la etapa S161, se puede realizar una generación de búfer de solapamiento en el dominio de tiempo XT-b(n) de la trama b. Por ejemplo:
[0049] En la etapa S162, se puede realizar una formación en ventanas del búfer de solapamiento en el dominio de tiempo. Por ejemplo:
[0050] En la etapa S163, se puede llevar a cabo una operación de adición con solapamiento para obtener muestras de tiempo reconstruidasifb(n)de la trama b. Por ejemplo:
[0051] En particular, la función de formación en ventanas wN(n) en el análisis (función de formación en ventanas de análisis) y la función de formación en ventanaswn (2N — 1 — n)en la síntesis (función de formación en ventanas de síntesis) se pueden definir de modo que se inviertan en el tiempo entre sí. Los coeficientes de la ventana de análisis y de la ventana de síntesis son versiones invertidas en el tiempo entre sí.
[0052] Se ha observado que una función de formación en ventanas particularmente efectiva (por ejemplo, la función de formación en ventanas de síntesis) puede ser una función de formación en ventanas de análisis que pre senta una parte serpenteante que intersecta con una función lineal en correspondencia con cuatro puntos.
[0053] La Figura 4 muestra una función de formación en ventanas de análisis 40. La función de formación en ventanas de análisis 40 se puede definir entre 0 y 2N, o entre 0 y un valor intermedio entre el 80 % y el 85 % o el 90 % de 2N (por ejemplo, 81,25 %). En algunos ejemplos, la función de formación en ventanas de análisis 40 se puede definir en un intervalo diferente (por ejemplo, más amplio).
[0054] La función de formación en ventanas de análisis 40 se define, al menos para una parte, con referencia a una función lineal 40'. En la Figura 4, la función lineal 40' es una función constante cuyo valor es 1. Sin embargo, En los ejemplos útiles para entender la invención, la función lineal 40' puede ser en general una función lineal, por ejemplo, definida en términos de y = an b, donde n es el índice entre 0 y 2N (o su parte distinta de cero) ya y b son constantes.
[0055] La función de formación en ventanas de análisis 40 comprende una parte de intersección (también denominada aquí parte serpenteante) 44. La parte serpenteante 44 es tal que la función de formación en ventanas 40 se encuentra y/o intersecta con la función lineal 40' en cuatro puntos #1, #2, #3, #4.
[0056] La parte serpenteante 44 puede ser tal que la función de formación en ventanas de análisis 40 sea diferente de la función lineal 40' en la mayoría de los índices, por ejemplo, para más del 99 % de los índices.
[0057] La parte serpenteante 44 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos (puntos de intersección #1, #2, #3, #4, el valor de la función de formación en ventanas de análisis 40 sea mayor que el valor de la función lineal (por ejemplo, 1) en el punto de intersección (#1, #2, #3 o #4) y, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de análisis 40 sea más pequeño que el valor de la función lineal en el punto de intersección.
[0058] La parte serpenteante 44 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos de intersección #1, #2, #3, #4, el valor de la función de formación en ventanas de análisis 40 sea menor que el valor de la función lineal (por ejemplo, 1) en el punto de intersección (#1, #2, #3 o #4) y, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de análisis 40 sea mayor que el valor de la función lineal en el punto de intersección.
[0059] La parte serpenteante 44 puede ser tal que cada uno de los puntos de intersección #1, #2, #3, #4 no sea inmediatamente consecutivo con los anteriores y los siguientes. Por ejemplo, entre dos puntos de intersección #1, #2, #3 y #4 hay al menos un índice de la función de formación en ventanas de análisis 40 cuyo valor no coincide con el valor de la función de formación en ventanas de análisis 40 en el mismo índice.
[0060] La función de formación en ventanas de análisis 40 se puede definir de manera que sea, en correspondencia con la parte serpenteante 44:
- mayor que la función lineal 40' en un primer intervalo 41 entre un primer punto de intersección #1 y un segundo punto de intersección #2;
- menor que la función lineal 40' en un segundo intervalo 42 entre el segundo punto de intersección #2 y un tercer punto de intersección #3;
- mayor que la función lineal 40' en un tercer intervalo 43 entre el tercer punto de intersección #3 y un cuarto punto de intersección #4.
[0061] El primer punto de intersección #1 puede preceder al segundo punto de intersección #2, que puede preceder al tercer punto de intersección #3, que puede preceder al cuarto punto de intersección #4.
[0062] La parte serpenteante 44 puede extenderse entre el primer y el último (por ejemplo, el cuarto) punto de intersección. Los puntos de intersección pueden ser sólo cuatro, en algunos ejemplos.
[0063] La función de formación en ventanas de análisis 40 puede comprender también una parte decreciente inicial 45, en la que se puede alcanzar un mínimo negativo. El mínimo negativo puede situarse entre el 6,25 % de 2N y el 18,75 % de 2n . La función de formación en ventanas de análisis 40 puede comprender también una parte rápidamente creciente 46 que aumenta rápidamente desde el mínimo negativo hacia la parte serpenteante 44 (por ejemplo, hacia el primer punto de intersección #1). La función de formación en ventanas de análisis 40 puede comprender también una parte rápidamente decreciente 47 que disminuye rápidamente de la parte serpenteante 44 a 0. La función de formación en ventanas de análisis 40 puede comprender también una parte constantemente cero 48 que puede comenzar entre el 80 % y el 85 % o el 90 % de 2N (tamaño de dos tramas) y continuar hasta el final de 2N.
[0064] El valor máximo absoluto 41' está en el primer intervalo 41 (o en el tercer intervalo).
[0065] La función de formación en ventanas de análisis 40 puede, en la parte serpenteante 44, presentar un valor máximo relativo 43' en el tercer intervalo 43 (o en el primer intervalo) y un valor mínimo relativo 42' en el segundo intervalo 42.
[0066] La función de formación en ventanas de análisis 40 puede, en la parte serpenteante 44, presentar los valores de la función de ventana serpenteante 40 en correspondencia con el segundo intervalo 42 superiores a 0,9. El segundo intervalo 42 puede estar por encima de 0,9.
[0067] La función de formación en ventanas de análisis 40 puede presentar, en la parte serpenteante 44, un valor más bajo que la función lineal 40' en un intervalo que consta del 30 % y del 50 % de dos tramas (2N). En los ejemplos, después del 50 % de dos tramas (2N), la función de ventana 40 puede ser mayor que la función lineal 40'. Por lo tanto, el punto #3 puede estar en correspondencia con el último índice de la primera trama o en correspondencia con el primer índice de la segunda trama. En el intervalo del 30 % al 50 % de dos tramas, la parte de ventana serpen teante 44 puede estar debajo de la función lineal.
[0068] El máximo 41' de la función de ventana serpenteante 44 puede ser de menos del 25 % (y preferiblemente menos del 5 % o 3 %) superior al valor de la función lineal 40' en el mismo índice n.
[0069] La función de formación en ventanas de análisis 40 puede presentar una primera diferenciación numé rica entre 0,02 y -0,02. La segunda diferenciación numérica puede estar entre -5*10-4 y 5*10-4, y preferiblemente entre -3*10-4 y 3*10-4. La tercera diferenciación numérica puede estar entre -2*10-5 y 2*10-5.
[0070] La función de formación en ventanas de análisis se define de modo que sea asimétrica.
[0071] En algunos ejemplos, la función de formación en ventanas de análisis puede ser tal que algunos de los intervalos (sub-segmentos) de la parte serpenteante 44 estén en orden inverso con respecto a la descripción anterior.
[0072]Las Figuras 26 y 27 muestran una función de análisis de ventana 40 (la Figura 27 es una vista ampliada de una parte de la Figura 26). La función de formación en ventanas de análisis 240 se puede definir entre 0 y 2N, o entre 0 y un valor intermedio entre el 80 % y el 85 % o el 90 % de 2N (por ejemplo, 81,25 %). En algunos ejemplos, la función de formación en ventanas de análisis 40 se puede definir en un intervalo diferente (por ejemplo, más amplio).
[0073]La función de formación en ventanas de análisis 40 se puede definir, al menos para una parte, con referencia a una función lineal 240'. Tal y como se muestra en la Figura 27, la función lineal 240' es una función constante cuyo valor es 1. La función lineal 40' puede ser, en los ejemplos útiles para entender la invención, una función lineal, por ejemplo, definida en términos de y = an b, donde n es el índice entre 0 y 2N (o su parte distinta de cero) y a y b son constantes (por ejemplo, a=0, b=1).
[0074]La función de formación en ventanas de análisis 240 comprende una parte de intersección (también denominada “parte serpenteante”) 244. La parte serpenteante 244 es tal que la función de formación en ventanas de análisis 240 se encuentra y/o intersecta con la función lineal 240' en cuatro puntos #1, #2, #3,#4.
[0075]La parte serpenteante 244 puede ser tal que la función de formación en ventanas de análisis 240 seadiferente de la función lineal 240' en la mayoría de los índices, por ejemplo, para más del 99 % de los índices.
[0076]La parte serpenteante 244 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos (puntos de intersección) #1, #2, #3, #4, el valor de la función de formación en ventanas de análisis 240 sea mayor que el valor de la función lineal 240’ en el punto de intersección (#1, #2, #3 o #4) y, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de análisis 240 sea más pequeño que el valor de la función lineal 240’ en el punto de intersección (#1, #2, #3 o #4).
[0077]La parte serpenteante 244 puede ser tal que, al menos en un índice que precede inmediatamente uno de los índices asociados a los puntos de intersección #1, #2, #3, #4, el valor de la función de formación en ventanas de análisis 40 sea menor que el valor de la función lineal 240’ en el punto de intersección (#1, #2, #3 o #4) y, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de análisis 40 sea mayor que el valor de la función lineal 240’ en el punto de intersección.
[0078]La parte serpenteante 244 puede ser tal que cada uno de los puntos de intersección #1, #2, #3, #4 no sea inmediatamente consecutivo con los anteriores y los siguientes. Por ejemplo, entre dos puntos de intersección #1, #2, #3 y #4 hay al menos un índice de la función de formación en ventanas de análisis 240 cuyo valor no coincide con el valor de la función de formación en ventanas de análisis 240 en el mismo índice.
[0079]La función de formación en ventanas de análisis 240 se puede definir de manera que sea, en corres pondencia con la parte serpenteante 244:
- mayor que la función lineal 240' en un primer intervalo 241 entre un primer punto de intersección #1 y un segundo punto de intersección #2;
- menor que la función lineal 240' en un segundo intervalo 242 entre el segundo punto de intersección #2 y un tercer punto de intersección #3;
- mayor que la función lineal 240' en un tercer intervalo 243 entre el tercer punto de intersección #3 y un cuarto punto de intersección #4.
[0080]El primer punto de intersección #1 precede al segundo punto de intersección #2, que precede al tercer punto de intersección #3, que precede al cuarto punto de intersección #4.
[0081]La parte serpenteante 244 puede extenderse entre el primer y el último (por ejemplo, el cuarto) punto de intersección. Los puntos de intersección pueden ser sólo cuatro, en algunos ejemplos.
[0082]La función de formación en ventanas de análisis 240 puede tener todos los valores positivos. El mínimo puede ser un valor 0, que puede estar en el primer índice de la función de formación en ventanas de análisis 240 y/o en los últimos índices de la función de formación en ventanas de análisis 240. La función de formación en ventanas de análisis 240 puede comprender una parte rápidamente creciente 246, que aumenta rápidamente hacia la parte serpenteante 244 (por ejemplo, el primer punto de intersección #1). La función de formación en ventanas de análisis 240 puede comprender también una parte rápidamente decreciente 247, que disminuye rápidamente desde la parte serpenteante 244 a 0. La función de formación en ventanas de análisis 240 puede comprender una parte constante mente cero 248, que puede comenzar entre el 84 % y el 90 % de 2N (tamaño de dos tramas) y continuar hasta el final de 2N.
[0083]El valor máximo absoluto 241' está en el primer intervalo 41 (o en el tercer intervalo).
[0084]La función de formación en ventanas de análisis 240 puede, en la parte serpenteante 244, presentar un valor máximo relativo 243' en el tercer intervalo 243 (o en el primer intervalo) y/o un valor mínimo relativo 242' en el segundo intervalo 242.
[0085]La función de formación en ventanas de análisis 240 puede, en la parte serpenteante 244, presentar los valores de la función de ventana serpenteante 240 en correspondencia con el segundo intervalo 242 mayor que 0,95. El segundo intervalo 242 puede estar por encima de 0,95. El primer y/o el tercer intervalo 241 y/o 243 pueden ser de menos de 1,05.
[0086]La función de formación en ventanas de análisis 240 puede presentar, en la parte serpenteante 244, un valor más bajo que la función lineal 240' en un intervalo que consta del 30 % y del 50 % de dos tramas (2N). En los ejemplos, después del 50 % de dos tramas (2N), la función de formación en ventanas 240 puede ser mayor que la función lineal 240'. Por lo tanto, el punto #3 puede estar en correspondencia con el último índice de la primera trama o en correspondencia con el primer índice de la segunda trama. En el intervalo del 30 % al 50 % de dos tramas, la parte de ventana serpenteante 244 puede estar debajo de la función lineal.
[0087]El máximo 241' de la función de ventana serpenteante 244 puede ser de menos del 25 % (y preferible mente menos del 5 % o 3 %) superior al valor de la función lineal 240' en el mismo índice n.
[0088]La función de formación en ventanas de análisis 240 puede presentar una primera diferenciación numérica entre -0,01 y 0,01. La segunda diferenciación numérica puede estar entre -10-4 y 10-4. La tercera diferenciación numérica puede estar entre -10-5 y 10-5.
[0089]La función de formación en ventanas de análisis se define de modo que sea asimétrica.
[0090]En algunos ejemplos, la función de formación en ventanas de análisis 240 puede ser tal que algunos de los intervalos (sub-segmentos) de la parte serpenteante 244 estén en orden inverso con respecto a la descripción más arriba.
[0091] Las Figuras 28 y 29 comparan las funciones de formación en ventanas de análisis 40 y 240.
[0092] La Figura 6 muestra otro ejemplo de la función de formación en ventanas de análisis 60 útil para enten der la invención. La Figura 7 muestra una vista ampliada de la función de formación en ventanas de análisis 60 en correspondencia con una parte serpenteante 64.
[0093] En este caso, la función de formación en ventanas de análisis 60 se puede definir, al menos para una parte, con referencia a una función lineal 60'. En la Figura 7, la función lineal 60' es una función decreciente lineal ("línea diagonal").
[0094] La parte serpenteante 64 puede ser tal que la función de formación en ventanas de análisis 60 se encuentre y/o intersecte con la función lineal 60' en cuatro puntos.
[0095] La función de formación en ventanas de análisis 40 se puede definir de modo que sea, en correspon dencia con la parte serpenteante 64:
- mayor que la función lineal 60' en un primer intervalo 61' entre un primer punto de intersección #1' y un segundo punto de intersección #2';
- menor que la función lineal 60' en un segundo intervalo 62' entre el segundo punto de intersección #2' y un tercer punto de intersección #3';
- mayor que la función lineal 60' en un tercer intervalo 63' entre el tercer punto de intersección #3' y un cuarto punto de intersección #4';
- menor que la función lineal 60' en un cuarto intervalo 64' entre el cuarto punto de intersección #4' y un quinto punto de intersección #5';
- mayor que la función lineal 60' en un quinto intervalo 65' entre el quinto punto de intersección #5' y un sexto punto de intersección #6'.
[0096] El valor máximo absoluto puede estar en el primer intervalo 61' (en otros ejemplos, por ejemplo, cuando la función lineal aumenta, puede estar en el quinto intervalo).
[0097] La función de formación en ventanas de análisis 60 puede presentar, en la parte serpenteante 64, un valor máximo relativo en el tercer intervalo 63' y/o en el quinto intervalo 65', estando un valor mínimo relativo en el segundo intervalo 62' y/o en el cuarto intervalo 64'.
[0098] La función de formación en ventanas de análisis 60 puede, en la parte serpenteante 64, presentar el valor de la función de formación en ventanas en correspondencia con al menos uno del primer y el tercer intervalo superior a 0,9 y en particular 0,95 (en otros ejemplos, por ejemplo, donde la función lineal aumenta, puede estar en el tercer y el quinto intervalo).
[0099] La función de formación en ventanas de análisis 60 puede presentar, en la parte serpenteante 64, un valor mayor que la función lineal 60' en un intervalo que consta del 30 % y del 50 % de dos tramas (2<n>).
[0100] El máximo de la función de ventana 60 puede ser de menos del 25 % (y preferiblemente menos del 5 %) mayor que el valor de la función lineal 60 en el mismo índice n.La función lineal 60' puede ser una función no creciente, en particular una función estrictamente decreciente.
[0101] La función de formación en ventanas de análisis se puede definir de modo que sea asimétrica.
[0102] En los ejemplos, la función de formación en ventanas de análisis puede presentar los intervalos que son invertidos con respecto a la Figura 6.
[0103] En los ejemplos, una función de formación en ventanas de síntesis se puede construir de modo que sea simétrica con respecto a la función de formación en ventanas de análisis. Por ejemplo, el eje de simetría puede estar en el centro del intervalo 2N (479 o 480, por ejemplo).
[0104] Un ejemplo de la función de formación en ventanas de síntesis 90 según la invención se proporciona en la Figura 9 (por ejemplo, la función de formación en ventanas de síntesis asociada a la función de formación en ven tanas de análisis 40 de la Figura 4). La función de formación en ventanas de síntesis 90 se puede definir entre 0 y 2N o entre un valor intermedio entre el 10 % o el 15 % y el 20 % de 2N y de 2N.
[0105] La función de formación en ventanas de síntesis 90 se define, al menos para una parte, con referencia a una función lineal, Tal y como se muestra en la Figura 9, la función lineal es una función constante cuyo valor es 1. Sin embargo, En los ejemplos útiles para entender la invención, la función lineal puede ser en general una función lineal, por ejemplo, definida en términos de y=an+b.
[0106] La función de formación en ventanas de síntesis 90 comprende una parte de intersección (también denominada “parte serpenteante”) 94. La parte serpenteante 94 es tal que la función de formación en ventanas de síntesis 90 se encuentra y/o intersecta con la función lineal 90' (constante 1, que sólo se muestra parcialmente por cuestiones de claridad) en cuatro puntos de intersección #1, #2, #3, #4 (siendo ilustrado sólo el #2). La función de formación en ventanas de síntesis puede intersectar con el valor 1 en el centro de la ventana (punto #2), es decir, entre la muestra N-1 y N.
[0107] La parte serpenteante 94 puede ser tal que la función de formación en ventanas de síntesis 90 sea diferente de la función lineal 90' en la mayoría de los índices, por ejemplo, para más del 99 % de los índices.
[0108] La parte serpenteante 94 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos #1, #2, #3, #4, el valor de la función de formación en ventanas de síntesis 90 sea mayor que el valor de la función lineal (por ejemplo, 1) en el punto (#1, #2, #3 o #4) y que, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto), el valor de la función de formación en ventanas de síntesis 90 sea menor que el valor de la función lineal en el punto de intersección. La parte serpenteante 94 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos #1, #2, #3, #4, el valor de la función de formación en ventanas de síntesis 90 sea menor que el valor de la función lineal en el punto (#1, #2, #3 o #4) y que, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de síntesis 90 sea mayor que el valor de la función lineal en el punto de intersección (#1, #2, #3 o #4).
[0109] La parte serpenteante 94 puede ser tal que cada uno de los puntos #1, #2, #3, #4 no sea inmediatamente consecutivo con otro de los puntos #1, #2, #3, #4. Por ejemplo, entre dos puntos de #1, #2, #3 y #4 puede existir al menos un índice de la función de formación en ventanas de síntesis 90 cuyo valor no coincida con el valor de la función de formación en ventanas de síntesis 90 en el mismo índice.
[0110] La función de formación en ventanas de síntesis 90 se define de modo que sea, en correspondencia con la parte serpenteante 94:
- mayor que la función lineal 90' en un primer intervalo 91 entre un primer punto de intersección #1 (no mostrado en la Figura 9, pero representable como simétrico al punto #4 en la Figura 4) y un segundo punto de intersección #2 (que, en este caso, está en la muestra n° 480, por ejemplo, en el centro del intervalo de 2N);
- menor que la función lineal 90' en un segundo intervalo 92 entre el segundo punto de intersección #2 y un tercer punto de intersección #3 (no mostrado en la Figura 9, pero representable como simétrico al punto #3 en la Figura 4); - mayor que la función lineal 90' en un tercer intervalo 93 entre el tercer punto de intersección #3 y un cuarto punto de intersección #4 (no mostrado en la Figura 9, pero representable como simétrico al punto #1 en la Figura 4).
[0111] La función de formación en ventanas de síntesis 90 comprende una parte constantemente cero 98 que puede situarse entre el 10 % y el 15 % de 2N. La función de formación en ventanas de síntesis 90 puede comprender también una parte rápidamente creciente 97 que aumenta rápidamente hacia la parte serpenteante 94 desde 0. La función de formación en ventanas de síntesis 90 puede comprender también una parte rápidamente decreciente 96 que disminuye rápidamente hacia un mínimo negativo desde la parte serpenteante 94. El mínimo negativo puede situarse entre el 81,25 % de 2N y el 93,7 % de 2N. La función de formación en ventanas de síntesis 90 puede com prender también una parte creciente final 95 que alcanza 0 desde el mínimo negativo.
[0112] El valor máximo absoluto puede estar en el tercer intervalo 93 (o en el primer intervalo).
[0113] La función de formación en ventanas de síntesis 90 puede, en la parte serpenteante 94, presentar un valor máximo relativo en el primer intervalo 91 (o en el tercer intervalo) y un valor mínimo relativo en el segundo intervalo.
[0114] La función de formación en ventanas de síntesis 90 puede, en la parte serpenteante 94, presentar el valor de la función de ventana serpenteante en correspondencia con al menos uno del primer y el tercer intervalo (91, 93) superior a 0,9. El tercer intervalo puede estar por encima de 0,9.
[0115] La función de formación en ventanas de síntesis 90 puede presentar, en la parte serpenteante 94, un valor mayor que la función lineal en un intervalo que consta del 30 % y del 50 % de dos tramas (2N).
[0116] El máximo de la función de formación en ventanas de síntesis 90 puede ser menos del 25 % (y preferiblemente menos del 5 %) superior al valor de la función lineal en el mismo índice n.
[0117] La función de formación en ventanas de síntesis 90 puede presentar una diferenciación numérica entre 0,02 y -0,02. La segunda diferenciación numérica puede estar entre -5 * l0 -4 y 5*10-4, y preferiblemente entre -3*10-4 y 3*10-4. La tercera diferenciación numérica puede estar entre -2*10-5 y 2*10-5.
[0118] La función lineal de síntesis 90 puede ser una función no creciente. En otros ejemplos, la función lineal de síntesis 90 puede ser una función no decreciente. La función lineal de síntesis 90 puede presentar un valor que es constante o varía en un máximo de 2 % o -2 %.
[0119] La función de formación en ventanas de síntesis 90 se define de modo que sea asimétrica.
[0120] En algunos ejemplos, la función de formación en ventanas de síntesis 90 puede ser una función simé trica con respecto a la forma mostrada en la Figura 9. Por ejemplo, el valor en 0 sería el valor que está en 960 en la Figura 9; el valor en 1 sería el valor que está en 959 en la Figura 9, y así sucesivamente.
[0121]Un ejemplo de la función de formación en ventanas de síntesis 290 se proporciona en la Figura 30 (por ejemplo, la función de formación en ventanas de síntesis asociada a la función de formación en ventanas de análisis 240 de las Figuras 26 a 29). La función de formación en ventanas de síntesis 290 se puede definir entre 0 y 2N o entre un valor intermedio entre el 10 % o el 15 % y el 20 % de 2N y 2N.
[0122]La función de formación en ventanas de síntesis 290 se define, al menos para una parte, con referencia a una función lineal 290’ (que es un valor constante 1).
[0123]En la Figura 30, la función lineal 290’ es una función constante cuyo valor es 1.
[0124]Sin embargo, la función lineal puede en general ser una función lineal, por ejemplo, definida en términos de y=an+b.
[0125]La función de formación en ventanas de síntesis 290 comprende una parte serpenteante 294. La parte serpenteante 294 es tal que la función de formación en ventanas de síntesis 290 se encuentre y/o intersecte con la función lineal 290' (constante 1, que solo se muestra parcialmente por cuestiones de claridad) en cuatro puntos de intersección #1, #2, #3, #4 (siendo ilustrado sólo el #2). La función de formación en ventanas de síntesis intersecta con el valor 1 en el centro de la ventana (punto #2), es decir, entre la muestra N-1 y N.
[0126]La parte serpenteante 294 puede ser tal que la función de formación en ventanas de síntesis 290 sea diferente de la función lineal 290' en la mayoría de los índices, por ejemplo, para más del 99 % de los índices.
[0127]La parte serpenteante 294 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos #1, #2, #3, #4, el valor de la función de formación en ventanas de síntesis 90 sea mayor que el valor de la función lineal (por ejemplo, 1) en el punto (#1, #2, #3 o #4) y que, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de síntesis 90 sea menor que el valor de la función lineal en el punto de intersección.
[0128]La parte serpenteante 294 puede ser tal que, al menos en un índice que precede inmediatamente a uno de los índices asociados a los puntos #1, #2, #3, #4, el valor de la función de formación en ventanas de síntesis 290 sea menor que el valor de la función lineal en el punto de intersección (#1, #2, #3 o #4) y que, al menos en el índice que sigue inmediatamente al mismo índice (asociado al punto de intersección), el valor de la función de formación en ventanas de síntesis 290 sea mayor que el valor de la función lineal en el punto de intersección (#1, #2, #3 o #4).
[0129]La parte serpenteante 294 puede ser tal que cada uno de los puntos de intersección #1, #2, #3, #4 no sea inmediatamente consecutivo con otro de los puntos #1, #2, #3, #4. Por ejemplo, entre dos puntos de intersección #1, #2, #3 y #4 puede existir al menos un índice de la función de formación en ventanas de síntesis 290 cuyo valor no coincida con el valor de la función de formación en ventanas de síntesis 290 en el mismo índice.
[0130]La función de formación en ventanas de síntesis 290 se define de modo que sea, en correspondenciacon la parte serpenteante 294:
- mayor que la función lineal 290' (por ejemplo, mayor que 1) en un primer intervalo 291 entre un primer punto de intersección #1 y un segundo punto de intersección #2 (que, en este caso, está en la muestra n. ° 480, por ejemplo, en el centro del intervalo de 2N);
- menor que la función lineal 290' en un segundo intervalo 292 entre el segundo punto de intersección #2 y un tercer punto de intersección #3;
- mayor que la función lineal 290' en un tercer intervalo 293 entre el tercer punto de intersección #3 y un cuarto punto de intersección #4.
[0131]La función de formación en ventanas de síntesis 290 puede comprender una parte constantemente cero 298, que puede situarse en un borde de la ventana (muestras 2N) y puede comprender entre el 10 % y el 15 % de las muestras. La función de formación en ventanas de síntesis 290 puede comprender también una parte rápidamente creciente 297 que aumenta rápidamente hacia la parte serpenteante 294 desde 0. La función de formación en ventanas de síntesis 290 puede comprender una parte rápidamente decreciente 296 que disminuye rápidamente hacia 0 desde la parte serpenteante 294.
[0132]El valor máximo absoluto puede estar en el tercer intervalo 293 (o en el primer intervalo).
[0133]La función de formación en ventanas de síntesis 290 puede, en la parte serpenteante 294, presentar un valor máximo relativo en el primer intervalo 291 (o en el tercer intervalo) y un valor mínimo relativo está en el segundo intervalo.
[0134]La función de formación en ventanas de síntesis 290 puede, en la parte serpenteante 294, presentar el valor de la función de ventana serpenteante en correspondencia con al menos uno del primer y el tercer intervalo (291, 293) mayor que 0,9 o 0,95. El tercer intervalo puede estar por encima de 0,95.
[0135]La función de formación en ventanas de síntesis 290 puede presentar, en la parte serpenteante 294, un valor mayor que la función lineal en un intervalo que consta del 30 % y del 50 % de dos tramas (2N).
[0136]El máximo de la función de formación en ventanas de síntesis 290 puede ser menos del 25 % (y prefe riblemente menos del 5 % o 3 %) mayor que el valor de la función lineal en el mismo índice n.
[0137]La función de formación en ventanas de síntesis 290 puede presentar una diferenciación numérica entre -0,01 y 0,01. La segunda diferenciación numérica puede estar entre-10-4y 10-4. La tercera diferenciación numérica puede estar entre -10 -5 y 10~5.
[0138]La función lineal de síntesis 90 puede ser una función no creciente. En otros ejemplos, la función lineal de síntesis 90 puede ser una función no decreciente. La función lineal de síntesis 90 puede presentar un valor que es constante o varía en un máximo de 2 % o -2 %.
[0139]La función de formación en ventanas de síntesis 90 se define de modo que sea asimétrica.
[0140]En algunos ejemplos, la función de formación en ventanas de síntesis 90 puede ser una función simétrica con respecto a la forma que se muestra en la Figura 9. Por ejemplo, el valor en 0 sería el valor que está en 960 en la Figura 9; el valor en 1 sería el valor que está en 959 en la Figura 9, y así sucesivamente.
5. Discusión
[0141] Se ha observado que esta función presenta características particularmente interesantes que son extre madamente adecuadas para las técnicas de MDCT (o MDST u otras) y de IMDCT (o IMDST u otras), en particular para la codificación de audio.
[0142] Como métrica para la suavidad de la forma de la ventana de MDCT, utilizamos la diferenciación numérica (derivado numérico) como:
w (t h) — w (t — h)
dw (t) = ----------- —-------------para t = h..2N — 1 — h
[0143] Otra métrica para evaluar la calidad de la ventana de MDCT es la forma temporal del error de cuantificación que se describe por:
Sq(t) = w2 (t N) w 2 (t ) para t = 0..N — 1
[0144] El error de cuantificación se puede introducir en el dominio espectral como parte de un proceso de codificación de audio.
[0145] La ventana ALDO se discute aquí. ALDO es una estrategia de diseño para ventanas asimétricas que proporciona una forma temporal mejorada. El proceso de diseño de la ventana ALDO tal y como se utiliza en el códec EVS se describe en (3GPP) y [2]. La Figura 1 muestra una forma de ventana esquemática para un esquema de ventana ALDO.
[0146] Una ventana ALDO consta de cuatro segmentos, una función creciente, una sección de estrictas, una función de decaimiento y ceros. El número de ceros en w4 determina también el número de ceros en w2, con w2 = 2*w4. La forma de obtener w1 y w3 se describe en [1] y [2].
[0147] La Figura 2 muestra una ventana ALDO diseñada según [1] y [2] para los parámetros Lz = 180 (número de ceros iniciales en la ventana de MDCT, W4(n) en la Figura 1) y la longitud total de la ventana es de 960 muestras.
[0148] Tal y como se puede ver en el cuarto gráfico secundario de la Figura 2 (“Error de cuantificación de modulación del tiempo”), la ventana ALDO muestra una buena forma temporal del error de cuantificación que significa que la suma de energía de dos ventanas de síntesis sucesivas que se solapan es próxima a uno. El resultado óptimo requeriría sólo aquellas que se logran mediante formas de ventanas simétricas.
[0149] Los inconvenientes de esta estrategia de diseño son visibles principalmente en el segundo gráfico se cundario de la Figura 2 (“Diferenciación numérica”), donde se describe la diferenciación numérica. Se puede ver que la forma de ventana no es una función matemática continuamente diferenciable y, por lo tanto, no es óptima en cuanto a la respuesta de frecuencia. Debido a los unos estáticos en la forma de ventana, no son posibles las transiciones suaves procedentes de la función de elevación y hacia la función de decaimiento.
[0150] La presente invención rompe con la restricción de diseño para mantener un segmento de estrictos unos con el fin de optimizar la forma temporal. En cambio, los unos son sustituidos por una secuencia de valores que serpentean alrededor de una función lineal (un valor constante, como "1"). Esta solución permite la forma suave y continua de la ventana mientras mantiene la forma temporal próxima a un estado óptimo.
[0151] La Figura 3 muestra un ejemplo de ventana diseñada con un segmento (parte) serpenteante según la invención. Tal y como se puede ver en el cuarto gráfico secundario de la Figura 3 (“Error de cuantificación de modu lación de tiempo”), la propiedad de la ventana en cuanto a la configuración temporal del error de cuantificación es similar a la ventana ALDO. Sin embargo, si se compara el segundo gráfico secundario de la Figura 3 ("Diferenciación numérica") con el segundo gráfico secundario de la Figura 2 (ventana ALDO), se puede entender que la invención permite generar formas de ventana que son continuamente diferenciables. Esto permite, por ejemplo, el diseño de formas de ventana con una mayor atenuación de banda de parada, lo que hasta ahora no era posible con el proceso de diseño utilizado para la ventana ALDO.
[0152] La Figura 4 describe un ejemplo de forma de ventana 40 en más detalle. En este ejemplo, el segmento serpenteante se basa en la intersección, en correspondencia con cuatro puntos, con una función lineal (un valor cons tante "1"). Incluso es posible un mayor número de intersecciones, pero se considera que cuatro es el número mínimo.
[0153] Tal ventana puede ser el resultado de un proceso de optimización matemático que combina una función de error para la respuesta de frecuencia con una función de error que representa la desviación a partir de la configu ración temporal óptima del ruido de cuantificación.
[0154] Algunas implementaciones requerían formatos de datos específicos, por ejemplo, implementaciones de punto fijo. Para tal implementación, el intervalo de valores de los coeficientes de ventana pueden ser escalas, dado que los valores superiores a uno requieren una escala diferente. En tales casos, el segmento serpenteante podría no estar alrededor de uno. Solo después de la anulación de puesta a escala, los valores entran en el intervalo obvio.
[0155] La Figura 5 muestra un ejemplo de cómo se representan los coeficientes de ventana de MDCT 50 dentro de una implementación de punto fijo. Es un ejemplo de representación donde algunos valores son puestos a escala por 2x y otros por 2x-1 debido a la arquitectura de punto fijo.
[0156] En los ejemplos útiles para entender la invención, la ventana no necesariamente serpentea alrededor de 1, pero puede serpentear alrededor de una línea diagonal virtual sin intersectar con el uno. La Figura 6 muestra tres ventanas diferentes, es decir:
- w1 Nuevo serpenteo optimizado alrededor de 1 (función de ventana 70);
- W2: Ventana G.718 (sin serpenteo en absoluto) (función de ventana 70');
- W3: Nueva ventana optimizada para casos especiales (ejemplo útil para entender la invención): serpenteo alrededor de una diagonal (función de ventana 60).
[0157] La ventana de MDCT descrita cumple con la propiedad de reconstrucción perfecta. Para eso, conside ramos que la MDCT se descompone como una operación de ventana, un paso de cancelación de alias en dominio de tiempo (TDAC) y un núcleo de tipo IV de transformación de coseno discreta (DCT), tal y como se describe en [3].
[0158] Por lo tanto, la formación en ventanas y TDAC pueden verse como una etapa de plegado en el lado de análisis y una etapa de desplegado en el lado de síntesis. En este último, las secuencias desplegadas de dos bloques se combinan en la operación de adición con solapamiento. Véase la Figura 8, que se refiere a un esquema de un bloque 1 (81) y de un bloque 2 (82).
[0159] Para la región de solapamiento en el lado de análisis, la formación en ventanas y TDAC del bloque 1 se pueden describir como:
y bloque 2
[0160] Para el lado de síntesis, P1 y P2 se despliegan, forman en ventanas, y se realiza la adición con solapamiento:
0(n)= Ws(N+n)Pi(n)+ws(n)P<2>(n) p a r a n=0...N-1
[0161] Esto se puede escribir como:
0(n)= wa(N+n)ws(N+n)-Wa(2N-1-n)ws(N+n)+Wa(n)ws(ri)+Wa(N-1-n)ws(n)
para n=0...N-1
que se puede separar en dos componentes:
PR1: Componente de reconstrucción perfecta
para n=0...N-1
- PR2: Componente de cancelación de alias
wa(N-1-n)ws(n)-Wa(2N-1-n)ws(N+n)=0
para n=0...N-1
[0162] Las Figuras 9-12 muestran secuencias de análisis y de síntesis.
[0163] A continuación, se hace referencia a las Figuras 19 y 20 con referencia a la diferenciación numérica de las funciones actuales de formación en ventanas de análisis y de síntesis.
[0164] Al considerar también la segunda y tercera diferenciación numérica, es posible distinguir claramente las propiedades de los presentes ejemplos (por ejemplo, la Figura 19 con referencia al ejemplo de la Figura 4, y la Figura 31 con referencia al ejemplo de la Figura 26) de aquellas de la técnica anterior (ALDO, Figura 20).
[0165] Como métrica para la suavidad de la forma de ventana de transformada con solapamiento modulada (por ejemplo, la forma de ventana de MDCT o MDST), podemos utilizar la diferenciación numérica como:
para t = h..2N — 1 — h
[0166] Para ponderar la importancia de cada coeficiente, es decir, las amplitudes más altas tienen un peso mayor, a continuación se describe una ponderación:
w (t h) w (t — h)
w dw (t) =dw(t) para t = h..2N — 1 — h
2
[0167] Esto permite omitir los coeficientes de ventana de bajo nivel en el análisis de la continuidad de la forma de la ventana.
[0168] En las Figuras 19 y 20 y 31, la primera diferenciación numérica se representa en la versión regular y ponderada (con guiones). 1902 y 3102 se refieren a la primera diferenciación numérica para la función de formación en ventanas de la invención; 1904 y 3104 (con guiones) se refieren a la versión ponderada de la primera diferenciación numérica para la función de formación en ventanas de la invención. 2002 se refiere a la primera diferenciación numérica para la función de formación en ventanas ALDO; 2004 (con guiones) se refiere a la versión ponderada de la primera diferenciación numérica para la función de formación en ventanas ALDO.
[0169] Para la segunda y tercera diferenciación numérica (ND), se utiliza la versión ponderada de la primera.
1910 y 3110 se refieren a la versión ponderada de la segunda diferenciación numérica para la función de formación en ventanas de la invención. 2010 se refiere a la versión ponderada de la segunda diferenciación numérica para la función de formación en ventanas ALDO. 1920 se refiere a la versión ponderada de la tercera diferenciación numérica para la función de formación en ventanas de la invención. 2020 y 3120 se refieren a la versión ponderada de la tercera diferenciación numérica para la función de formación en ventanas ALDO.
[0170] Tal y como se puede observar, la segunda versión ND muestra algunos picos claros 2021 para la ven<tana ALDO mientras que las ventanas de la invención muestran sólo cambios moderados. Para la tercera>N<d>,<también>el nivel de amplitud de ambas ventanas se diferencia claramente y se puede expresar.
[0171] Aquí se presenta un análisis del grado de libertad para el diseño de ventana para ALDO y para la función de ventana de la invención.
[0172] La estrategia de diseño de ALDO [2] ofrece sólo los parámetros C1, C2 y el número de ceros Lz como grado de libertad. Cualquier estrategia relacionada con la atenuación de campo cercano o campo lejano no es posible con el procedimiento propuesto, dado que el grado de libertad dado en el proceso de diseño es muy limitado.
[0173] Para extender el algoritmo ALDO y permitir un mayor grado de libertad, se debe abandonar la estrategia de diseño en [2] y se debe cambiar por un procedimiento de optimización numérica. En una primera etapa, el segmento de los estrictos unos en el centro de la ventana se mantiene, mientras se optimizan los coeficientes de ventana libres (o el parámetro de diseño).
[0174] Suponiendo que las ventanas de análisis y de síntesis son siempre versiones invertidas en el tiempo entre sí, la restricción de reconstrucción perfecta puede expresarse mediante:
Wa(N+n)ws(N+n)+Wa(n)ws(n)=1 para n=0...N-1
[0175] Esto puede cumplirse siempre restringiendo el número de coeficientes libres a 1,5N, por ejemplo, me diante:
[0176] El segmento de ceros se encuentra dentro de w(2N-n). Para la restricción de los estrictos unos en el centro, 2*Lz de los coeficientes de ventana son considerados coeficientes no libres. Para una longitud de transforma ción de N = 480 y un tamaño de ventana de 2N y Lz = 180, esto conduce a un grado de libertad de 1,5N-2*Lz = 360 coeficientes libres. Esta ventana se denomina ventana intermedia.
[0177] La nueva invención aumenta el grado de libertad al máximo al intercambiar la parte de los estrictos unos por un segmento serpenteante (por ejemplo, 44, 64, 94) alrededor de uno o alrededor de cualquier otra línea recta (por ejemplo, diagonal) (por ejemplo, 40', 60', 90'). Por lo tanto, sólo la mitad del segmento central se debe excluir de los coeficientes libres. Por consiguiente, el número de coeficientes disponibles se incrementa a 1,5*480-180 = 540 coeficientes libres. Esto permite optimizar al máximo la respuesta de frecuencia hacia cualquier enfoque marcado.
[0178 Las Figuras 21 y 22 muestran una comparación de las estrategias de diseño. En particular, la Figura 2 l muestra una forma de ventana de comparación ALDO (211) frente a una intermedia (212) frente a la nueva inven ción (213). La Figura 22 muestra un zoom (vista ampliada) de las formas de ventana ALDO (211), intermedia (212) y de la nueva invención (213).
[0179] La ventana intermedia y la ventana de la nueva invención se optimizan hacia el mismo enfoque.
[0180] La Figura 23 muestra una respuesta de frecuencia de trazado con ALDO (231), intermedia (232) y nueva invención (233). La ventana intermedia (231) y la de la nueva invención (233) pueden enfocarse en diferentes zonas, logrando en este caso una mejor atenuación de campo lejano. Esto es necesario, por ejemplo, para evitar distorsiones de alias causadas por señales de banda limitada o cuando las señales son remuestreadas a través de un banco de filtros. Este enfoque es imposible para la ventana ALDO, dado que sólo hay dos parámetros disponibles que controlan la forma. Si comparamos la ventana intermedia y la de la nueva invención, se hace evidente que la nueva invención logra muchas menos fluctuaciones en la respuesta debido a la forma muy continua en el dominio de tiempo.
[0181] La Figura 24 muestra un zoom (vista ampliada) de la respuesta de frecuencia que compara la ventana intermedia (242) y la de la nueva invención (243). Tal y como se puede observar, la ventana de la nueva invención (243) muestra siempre una atenuación significativa mayor de todos los lóbulos laterales. Esto confirma que la parte serpenteante (44, 64, 94) es beneficiosa en el diseño de la ventana sobre una parte de los estrictos unos.
[0182] Con referencia a la modulación temporal de la ventana, se observa que la motivación principal de la ventana ALDO fue combinar una forma asimétrica con una amplitud máxima de 1, para evitar grandes fluctuaciones temporales del error de cuantificación. El error de cuantificación se añade en el dominio de frecuencia y su forma temporal se controla mediante la forma de la ventana de síntesis.
[0183] En realidad, aquí también la secuencia serpenteante mejora incluso esta propiedad de la ventana. La Figura 25 muestra una comparación directa de la modulación temporal del error de cuantificación causado por una ventana ALDO (253) y una según la invención propuesta (251). Tal y como se puede ver, la distorsión temporal máxima es menor para la nueva invención y, por lo tanto, proporciona distorsiones menos notables.
[0184] En los ejemplos más arriba, la parte serpenteante puede estar, por ejemplo, en correspondencia (al menos parcial) con el núcleo de DCT. En los ejemplos, al menos un primer punto de intersección (por ejemplo, #1) está en la primera trama, mientras que al menos otro punto de intersección (por ejemplo, #3) está en la trama siguiente. En los ejemplos, un punto de intersección (por ejemplo, #2) está en el borde entre la primera trama y la trama siguiente.
[0185] En los ejemplos, "serpentear" se refiere al hecho de que hay al menos cuatro intersecciones con una función lineal (la parte serpenteante intersecta con la función lineal en al menos dos o en algunos casos en al menos cuatro puntos). Por ejemplo, una parte serpenteante puede presentar una parte creciente, seguida de una parte de creciente, seguida de una parte creciente y así sucesivamente, o una parte decreciente, seguida de una parte creciente, seguida de una parte decreciente, y así sucesivamente.
6. Otros ejemplos
[0186] La Figura 17 muestra un aparato 110 que puede implementar el aparato codificador 130 (o 130A) y/o la herramienta de MDCT 131 y/o realizar al menos algunas etapas del procedimiento 150. El aparato 110 comprende un procesador 111 y una unidad de memoria no transitoria 112 con un bloque 114 que almacena instrucciones que, cuando son ejecutadas por el procesador 111, pueden hacer que el procesador 111 realice una síntesis de MDCT. La unidad de memoria no transitoria 112 puede almacenar también el bloque 113, una función de formación en ventanas de análisis, por ejemplo, tal y como se ha discutido más arriba. El aparato 110 puede comprender una unidad de entrada 116 que puede obtener una señal de información de entrada (por ejemplo, una señal de audio). Se puede reservar un espacio de almacenamiento transitorio 118 para salvaguardar los datos que se van a actualizar (por ejem plo, búferes de entrada).
[0187] La Figura 18 muestra un aparato 120 que puede implementar el aparato decodificador 140 (o 140A) y/o el IMDCT 147 y/o realizar el procedimiento 160. El aparato 120 comprende un procesador 121 y una unidad de me moria no transitoria 122 con un bloque 124 que almacena instrucciones que, cuando son ejecutadas por el procesador 121, hacen que el procesador 121 realice, entre otras cosas, un proceso de síntesis de MDCT. El aparato 120 puede comprender una unidad de entrada 126 que puede obtener una representación decodificada de una señal de informa ción (por ejemplo, una señal de audio) en el FD. Por lo tanto, el procesador 121 puede realizar procesos para obtener una representación en el TD de la señal de información. Esta representación decodificada se puede proporcionar a unidades externas mediante una unidad de salida 127. La unidad de salida 127 puede comprender, por ejemplo, una unidad de comunicación para comunicar con dispositivos externos (por ejemplo, mediante una comunicación inalám brica, tal como Bluetooth) y/o espacios de almacenamiento externos. El procesador 121 puede salvaguardar la repre sentación decodificada de la señal de audio en un espacio de almacenamiento local 128.
[0188] En los ejemplos, el aparato 110 y 120 puede ser el mismo dispositivo. En los ejemplos, los aparatos 110 y 120 intercambian señales de información y/o datos de control, por ejemplo, de forma inalámbrica, por ejemplo, me diante el protocolo Bluetooth.
[0189] En función de ciertos requisitos de implementación, los ejemplos pueden implementarse en hardware. La implementación puede realizarse mediante un medio de almacenamiento digital, por ejemplo, un disquete, un Disco Versátil Digital (DVD), un Disco Blu-Ray, un Disco Compacto (CD), una Memoria de sólo Lectura (ROM), una Memoria de sólo Lectura Programable (PROM), una Memoria de sólo Lectura Borrable y Programable (EPROM), una Memoria de sólo Lectura Eléctricamente Borrable y Programable (EEPROM) o una memoria flash, que presentan señales de control legibles electrónicamente almacenadas en las mismas, que cooperan (o son capaces de cooperar) con un sistema informático programable de tal modo que se realice el procedimiento respectivo. Por lo tanto, el medio de almacenamiento digital puede ser legible por ordenador.
[0190] En general, los ejemplos pueden implementarse como un producto de programa de ordenador con instrucciones de programa, siendo las instrucciones de programa operativas para realizar uno de los procedimientos cuando el producto de programa de ordenador se ejecuta en un ordenador. Las instrucciones de programa pueden, por ejemplo, almacenarse en un medio legible por máquina.
[0191] Otros ejemplos comprenden el programa de ordenador para realizar uno de los procedimientos descritos en esta invención, almacenado en un soporte legible por máquina. En otras palabras, un ejemplo de procedimiento es, por lo tanto, un programa de ordenador que presenta una instrucción de programa para realizar uno de los proce dimientos descritos en esta invención, cuando el programa de ordenador se ejecuta en un ordenador.
[0192] Otro ejemplo de los procedimientos es, por lo tanto, un medio de soporte de datos (o un medio de almacenamiento digital, o un medio legible por ordenador) que comprende, grabado en el mismo, el programa de ordenador para realizar uno de los procedimientos descritos en esta invención. El medio de soporte de datos, el medio de almacenamiento digital o el medio grabado son tangibles y/o no transitorios, en lugar de señales que son intangibles y transitorias.
[0193] Otro ejemplo comprende una unidad de procesamiento, por ejemplo, un ordenador, o un dispositivo lógico programable que realiza uno de los procedimientos descritos en esta invención.
[0194] Otro ejemplo comprende un ordenador que presenta, instalado en el mismo, el programa de ordenador para realizar uno de los procedimientos descritos en esta invención.
[0195] Otro ejemplo comprende un aparato o un sistema que transfiere (por ejemplo, electrónica u ópticamente) a un receptor un programa de ordenador para realizar uno de los procedimientos descritos en esta invención. El re ceptor puede ser, por ejemplo, un ordenador, un dispositivo móvil, un dispositivo de memoria o similar. El aparato o sistema puede comprender, por ejemplo, un servidor de archivos para transferir el programa de ordenador al receptor.
[0196] En algunos ejemplos, se puede utilizar un dispositivo lógico programable (por ejemplo, una matriz de puertas programable por campo) para realizar algunas o todas las funcionalidades de los procedimientos descritos en esta invención. En algunos ejemplos, una matriz de puertas programable por campo puede cooperar con un micropro cesador para realizar uno de los procedimientos descritos en esta invención. En general, los procedimientos pueden ser realizados por cualquier aparato de hardware apropiado.
[0197] Los ejemplos descritos más arriba son ilustrativos de los principios discutidos más arriba. Se entiende que las modificaciones y variaciones de las disposiciones y los detalles descritos en esta invención serán evidentes. Por lo tanto, la intención es que la invención esté limitada por el alcance de las reivindicaciones de patente adjuntas y no por los detalles específicos presentados a modo de descripción y de explicación de los ejemplos dados en esta invención.
7. Algunos ejemplos de funciones de formación en ventanas
[0198] Aquí se proporcionan ejemplos numéricos. Dado que no se ha encontrado ninguna fórmula matemática en forma cerrada para obtener la función, a continuación se proporcionan ejemplos. Los valores que se incluyen a continuación pueden proporcionarse en orden hacia atrás o en orden hacia delante, en el sentido de que en algunos ejemplos el primer valor está asociado al momento n = 0 y el último valor está asociado al último momento n = 2N-1 (dirección hacia delante), mientras que en algunos ejemplos, el primer valor está asociado al instante de tiempo n = 2N-1 y el último valor está asociado al primer momento n = 0 (dirección hacia atrás). En algunos casos, la función de formación en ventanas de análisis y la función de formación en ventanas de síntesis se toman de la misma lista, pero la función de formación en ventanas de análisis se lee en la dirección hacia atrás (o hacia delante), mientras que la función de formación en ventanas de síntesis se lee en la dirección hacia delante (o hacia atrás).
[0199] Para representar al menos uno de los ejemplos a continuación, es posible extraer una sub-sucesión de al menos 10 valores (por ejemplo, valores consecutivos), cuando los 10 valores son diferentes de 0 (por ejemplo, todas las muestras o al menos la mayoría de ellas pueden formar los al menos 10 valores). Una tolerancia de ± 1 % puede ser posible; en algunos casos ± 0,5 %, ± 0,05 %, en otros casos, ± 2 %, ± 5 %, en otros casos 0 %.
7.1 Ejemplos asociados a las Figuras 4 y 9
[0200] En los ejemplos, una notación tal como -7.078546706512391e-04f significa -7.078546706512391*10-4. "f" se refiere a la notación en punto flotante (en algunos casos, se puede omitir).
[0201] Un ejemplo numérico de función de formación en ventanas W80, para el tamaño de trama N=80 se pro porciona aquí por las 160 entradas para n = 0 ... 2N-1. Tal y como se explicó más arriba, los últimos valores pueden ser constantemente 0.
-7.078546706512391e-04f, -2.098197727900724e-03f, -4.525198076002370e-03f, -8.233976327300612e-03f, -1.337713096257934e-02f, -1.999721557401502e-02f, -2.800909464274782e-02f, -3.721502082245055e-02f, -4.731768261606175e-02f, -5.794654834034055e-02f, -6.867606753531441e-02f, -7.904647440788692e-02f, -8.859705468085925e-02f, -9.688303623049199e-02f, -1.034961241263523e-01f, -1.080766457616878e-01f, -1.103242262600913e-01f, -1.099809851424550e-01f, -1.068172142230882e-01f, -1.006190418791648e-01f, -9.116452506492527e-02f, -7.820617483254730e-02f, -6.146688124166948e-02f, -4.063362855701623e-02f, -1.536329520788766e-02f, 1.470155068746303e-02f, 4.989736509080558e-02f, 9.050369257152079e-02f, 1.366911019414417e-01f, 1.884686389218322e-01f, 2.456456803467095e-01f, 3.077789078889820e-01f, 3.741642373060188e-01f, 4.438114799213576e-01f, 5.154735456539700e-01f, 5.876661722564289e-01f, 6.587619767809000e-01f, 7.270576699841359e-01f, 7.908752989295335e-01f, 8.486643364959733e-01f, 8.991320235484349e-01f, 9.413348145272842e-01f, 9.747634827941575e-01f, 9.994114730415857e-01f, 1.015760373791603e+00f, 1.024736164069697e+00f, 1.027634294456205e+00f, 1.025991493983836e+00f, 1.021427210603284e+00f, 1.015439859549357e+00f, 1.009366925499550e+00f, 1.003508162416449e+00f, 9.988898206257559e-01f, 9.953133902427869e-01f, 9.925943919208190e-01f, 9.905771957917731e-01f, 9.891371616557014e-01f, 9.881790747212391e-01f, 9.876249269174586e-01f, 9.874056275509585e-01f, 9.874524849192456e-01f, 9.876951134084213e-01f, 9.880640617030884e-01f, 9.884926873551375e-01f, 9.889230031022089e-01f, 9.893074965384659e-01f, 9.896146331889107e-01f, 9.898319269347060e-01f, 9.899693102025342e-01f, 9.900603352632121e-01f, 9.901575015155720e-01f, 9.903255289051605e-01f, 9.906303787150326e-01f, 9.911298894709990e-01f, 9.918665491182922e-01f, 9.928619727154252e-01f, 9.941156069136238e-01f, 9.956033775539884e-01f, 9.972793109558521e-01f, 9.990784840729244e-01f, 1.000922365901945e+00f, 1.002728111386909e+00f, 1.004416038098237e+00f, 1.005919224127911e+00f, 1.007189345025525e+00f, 1.008200146369426e+00f, 1.008949493525753e+00f, 1.009458241425143e+00f, 1.009768980817384e+00f, 1.009940336228694e+00f, 1.010039453539107e+00f, 1.010132323996401e+00f, 1.010272524848519e+00f, 1.010494354532353e+00f, 1.010808068774316e+00f, 1.011201071127927e+00f, 1.011641272406023e+00f, 1.012080125934687e+00f, 1.012458183122033e+00f, 1.012706955800289e+00f, 1.012755013843985e+00f, 1.012530134411619e+00f, 1.011962331100864e+00f, 1.010982135506986e+00f, 1.009512438049510e+00f, 1.007460860286395e+00f, 1.004708677491086e+00f, 1.001111413242302e+00f, 9.965041017623596e-01f, 9.907199995730845e-01f, 9.823765865983288e-01f, 9.708821747608998e-01f, 9.546732976073705e-01f, 9.321553861564006e-01f, 9.018003682081348e-01f, 8.623984077953557e-01f, 8.132817365236141e-01f, 7.544551974836834e-01f, 6.866580716267418e-01f, 6.113488038789190e-01f, 5.306181649316597e-01f, 4.471309850999502e-01f, 3.639114681156236e-01f, 2.841647033392408e-01f, 2.110209448747969e-01f, 1.472287968327703e-01f, 9.482665349502291e-02f, 5.482436608328477e-02f, 2.701461405056264e-02f, 9.996743588367519e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f
[0202] Un ejemplo numérico de función de formación en ventanas W160, para el tamaño de trama N=160 se proporciona aquí por las 320 entradas para n = 0 ... 2N-1. Tal y como se explicó más arriba, los últimos valores pueden ser constantemente 0.
-4.619898752628163e-04f, -9.747166718929050e-04f, -1.664473096973725e-03f, -2.597106916737789e-03f, -3.806285163352241e-03f, -5.324608721716763e-03f, -7.175885277771099e-03f, -9.382480860899108e-03f, -1.195270300743193e-02f, -1.489528159506296e-02f, -1.820666399965468e-02f, -2.187570925786862e-02f, -2.588471937157619e-02f, -3.020862738245264e-02f, -3.481597793538342e-02f, -3.967067992672979e-02f, -4.472698045914417e-02f, -4.994225863256500e-02f, -5.526334794593565e-02f, -6.063717235243996e-02f, -6.600961519440657e-02f, -7.131966266443390e-02f, -7.651178225890490e-02f, -8.152964005319532e-02f, -8.631137544905677e-02f, -9.080411291245728e-02f, -9.495377758870335e-02f, -9.870736514214426e-02f, -1.020202684361974e-01f, -1.048438825017798e-01f, -1.071382314127799e-01f, -1.088690135027248e-01f, -1.099969655786929e-01f, -1.104898474883336e-01f, -1.103225838568563e-01f, -1.094621746650760e-01f, -1.078834293141886e-01f, -1.055612509762041e-01f, -1.024650162703341e-01f, -9.857014566194629e-02f, -9.384684920715425e-02f, -8.826309993000785e-02f, -8.178792716809512e-02f, -7.438785600211463e-02f, -6.602189797715241e-02f, -5.665655641133161e-02f, -4.624456893420224e-02f, -3.474585776145929e-02f, -2.211581608120528e-02f, -8.310425696208936e-03f, 6.717697635290676e-03f, 2.300642061077823e-02f, 4.060106462625085e-02f, 5.953239090915557e-02f, 7.983354189816511e-02f, 1.015233140203748e-01f, 1.246171387327525e-01f, 1.491152519299797e-01f, 1.750067399059861e-01f, 2.022699854906251e-01f, 2.308655379767671e-01f, 2.607365124918583e-01f, 2.918144694729168e-01f, 3.240095704645023e-01f, 3.572175180786021e-01f, 3.913146885756875e-01f, 4.261571642320424e-01f, 4.615925445090212e-01f, 4.974471592901086e-01f, 5.335326819631583e-01f, 5.696546730080154e-01f, 6.056083823929643e-01f, 6.411830842823245e-01f, 6.761653499550255e-01f, 7.103400549562944e-01f, 7.434943718765665e-01f, 7.754281892901473e-01f, 8.059437233154637e-01f, 8.348589373399948e-01f, 8.620108336276733e-01f, 8.872599706865123e-01f, 9.104863121445679e-01f, 9.315962496426278e-01f, 9.505220861927248e-01f, 9.672366712325431e-01f, 9.817397501303696e-01f, 9.940557180662704e-01f, 1.004247514102417e+00f, 1.012407428282884e+00f, 1.018650990561848e+00f, 1.023118841384460e+00f, 1.025972450969440e+00f, 1.027397523939210e+00f, 1.027585830688143e+00f, 1.026738673647482e+00f, 1.025061777648234e+00f, 1.022756514615106e+00f, 1.020009139549275e+00f, 1.016996499560845e+00f, 1.013915946100629e+00f, 1.011044869639164e+00f, 1.007773858455400e+00f, 1.004848753962734e+00f, 1.002245009135684e+00f, 9.999393169239009e-01f, 9.979055415627330e-01f, 9.961203379971326e-01f, 9.945597525471822e-01f, 9.932031606606762e-01f, 9.920297273323891e-01f, 9.910230654424902e-01f, 9.901668953434221e-01f, 9.894488374513719e-01f, 9.888556356037892e-01f, 9.883778520531268e-01f, 9.880051626345804e-01f, 9.877295459610343e-01f, 9.875412739766566e-01f, 9.874329809802893e-01f, 9.873949921033299e-01f, 9.874197049003676e-01f, 9.874973205882319e-01f, 9.876201238703241e-01f, 9.877781920433015e-01f, 9.879637979933339e-01f, 9.881678007807095e-01f, 9.883835200189653e-01f, 9.886022219397892e-01f, 9.888182771263505e-01f, 9.890247977602895e-01f, 9.892178658748239e-01f, 9.893923680007577e-01f, 9.895463342815009e-01f, 9.896772011542693e-01f, 9.897859195209235e-01f, 9.898725363809847e-01f, 9.899410789223559e-01f, 9.899945557067980e-01f, 9.900394023736973e-01f, 9.900814722948890e-01f, 9.901293790312005e-01f, 9.901902265696609e-01f, 9.902734448815004e-01f, 9.903862280081246e-01f, 9.905379830873822e-01f, 9.907348826312993e-01f, 9.909842592301273e-01f, 9.912905118607647e-01f, 9.916586940166509e-01f, 9.920906151219310e-01f, 9.925887208794144e-01f, 9.931516528513824e-01f, 9.937790866568735e-01f, 9.944668184371617e-01f, 9.952116634297566e-01f, 9.960068616185641e-01f, 9.968461329825753e-01f, 9.977203369515556e-01f, 9.986213520769593e-01f, 9.995382582242990e-01f, 1.000461955079660e+00f, 1.001380551217109e+00f, 1.002284871786226e+00f, 1.003163845364970e+00f, 1.004009147462043e+00f, 1.004811375053364e+00f, 1.005563968008037e+00f, 1.006259855360867e+00f, 1.006895570408563e+00f, 1.007466616298057e+00f, 1.007972441990187e+00f, 1.008411468616852e+00f, 1.008786009787269e+00f, 1.009097763850333e+00f, 1.009351762546296e+00f, 1.009552401900961e+00f, 1.009707093778162e+00f, 1.009822090220407e+00f, 1.009906958448099e+00f, 1.009969021400474e+00f, 1.010017890428877e+00f, 1.010060809299530e+00f, 1.010106564965965e+00f, 1.010161131093372e+00f, 1.010231078494249e+00f, 1.010319484524512e+00f, 1.010430470494512e+00f, 1.010564099281000e+00f, 1.010721360243234e+00f, 1.010899655674578e+00f, 1.011096993993037e+00f, 1.011308167670753e+00f, 1.011529185153809e+00f, 1.011753008569803e+00f, 1.011973876511603e+00f, 1.012182837094955e+00f, 1.012373028737774e+00f, 1.012535058602453e+00f, 1.012660975529858e+00f, 1.012740575296603e+00f, 1.012765922449960e+00f, 1.012726958954961 e+00f, 1.012615904116265e+00f, 1.012422888521601e+00f, 1.012140460211194e+00f, 1.011758810583150e+00f, 1.011269960947744e+00f, 1.010663676735228e+00f, 1.009930754807923e+00f, 1.009058249873833e+00f, 1.008034308295421 e+00f, 1.006843352506855e+00f, 1.005470005637052e+00f, 1.003894772403371 e+00f, 1.002098854400575e+00f, 1.000060686758758e+00f, 9.977600196406868e-01f, 9.951746430061121e-01f, 9.922861082472264e-01f, 9.890757868707590e-01f, 9.847362453480265e-01f, 9.798613526271561e-01f, 9.741378617337759e-01f, 9.673331975559332e-01f, 9.592539757044516e-01f, 9.496984081652284e-01f, 9.384634163826711e-01f, 9.253567968750328e-01f, 9.101986790930605e-01f, 8.928338316495705e-01f, 8.731437835983047e-01f, 8.510420440685049e-01f, 8.264839911291133e-01f, 7.994681492797084e-01f, 7.700431275216928e-01f, 7.383028603058783e-01f, 7.043814340356083e-01f, 6.684616478236647e-01f, 6.307755329382612e-01f, 5.915799587176216e-01f, 5.511703155400274e-01f, 5.098915423728179e-01f, 4.681017110047964e-01f, 4.26177297149301 0e-01f, 3.845172335531009e-01f, 3.435228672445613e-01f, 3.036004651973099e-01f, 2.651434678028531e-01f, 2.285283969438072e-01f, 1.941021906320984e-01f, 1.621735416384830e-01f, 1.330015240938615e-01f, 1.067840430193724e-01f, 8.365057236623041e-02f, 6.365188111381356e-02f, 4.676538412257621e-02f, 3.288072750732215e-02f, 2.183057564646270e-02f, 1.336381425803019e-02f, 6.758124889697787e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, +0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+oof, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f
[0203] Un ejemplo numérico de función de formación en ventanas W240, para el tamaño de trama N = 240 se proporciona aquí (480 muestras):
-3.613496418928369e-04f, -7.078546706512391e-04f, -1.074443637110903e-03f, -1.533478537964509e-03f, -2.098197727900724e-03f, -2.778420871815740e-03f, -3.584129920673041e-03f, -4.525198076002370e-03f, -5.609327243712055e-03f, -6.843234536105624e-03f, -8.233976327300612e-03f, -9.785314755557023e-03f, -1.149880303071551e-02f, -1.337713096257934e-02f, -1.542181679511618e-02f, -1.762979910961727e-02f, -1.999721557401502e-02f, -2.252080561390149e-02f, -2.519406300389030e-02f, -2.800909464274782e-02f, -3.095765092956728e-02f, -3.402996266948349e-02f, -3.721502082245055e-02f, -4.050053247568393e-02f, -4.387219218706189e-02f, -4.731768261606175e-02f, -5.082325342672667e-02f, -5.437166635159518e-02f, -5.794654834034055e-02f, -6.153426201732499e-02f, -6.511708163113709e-02f, -6.867606753531441e-02f, -7.219447805250771e-02f, -7.565695975592170e-02f, -7.904647440788692e-02f, -8.234442557322251e-02f, -8.553324579905185e-02f, -8.859705468085925e-02f, -9.152091100798199e-02f, -9.428847446755965e-02f, -9.688303623049198e-02f, -9.929123258537813e-02f, -1.015008467688577e-01f, -1.034961241263523e-01f, -1.052637003544443e-01f, -1.067939984687745e-01f, -1.080766457616878e-01f, -1.090997300590506e-01f, -1.098524491515805e-01f, -1.103242262600913e-01f, -1.105084619148789e-01f, -1.103977408741932e-01f, -1.099809851424550e-01f, -1.092492774392824e-01f, -1.081974227416502e-01f, -1.068172142230882e-01f, -1.050995803285455e-01f, -1.030360111111103e-01f, -1.006190418791648e-01f, -9.784120023411771e-02f, -9.469304216883027e-02f, -9.116452506492527e-02f, -8.724644532866996e-02f, -8.293043914044632e-02f, -7.820617483254730e-02f, -7.306142427456862e-02f, -6.748468182105991e-02f, -6.146688124166948e-02f, -5.499497258200362e-02f, -4.805444424454820e-02f, -4.063362855701623e-02f, -3.272045590229335e-02f, -2.430122582451853e-02f, -1.536329520788766e-02f, -5.891434269890659e-03f, 4.126595858583295e-03f, 1.470155068746303e-02f, 2.584738191459814e-02f, 3.757652772246801e-02f, 4.989736509080558e-02f, 6.282034030592902e-02f, 7.635397728566121e-02f, 9.050369257152079e-02f, 1.052747118478660e-01f, 1.206703467513333e-01f, 1.366911019414417e-01f, 1.533343890681390e-01f, 1.705954709184399e-01f, 1.884686389218322e-01f, 2.069449962574092e-01f, 2.260093000067393e-01f, 2.456456803467095e-01f, 2.658346019332584e-01f, 2.865543814049772e-01f, 3.077789078889820e-01f, 3.294769437072290e-01f, 3.516171481750350e-01f, 3.741642373060188e-01f, 3.970739591211551e-01f, 4.203043046885219e-01f, 4.438114799213576e-01f, 4.675442291623012e-01f, 4.914498631045615e-01f, 5.154735456539700e-01f, 5.395557644293222e-01f, 5.636399817032525e-01f, 5.876661722564289e-01f, 6.115695310143157e-01f, 6.352890592874099e-01f, 6.587619767809000e-01f, 6.819230974423550e-01f, 7.047092819314779e-01f, 7.270576699841359e-01f, 7.489068963384272e-01f, 7.701990187606995e-01f, 7.908752989295335e-01f, 8.108788692151807e-01f, 8.301579139160681e-01f, 8.486643364959733e-01f, 8.663548164329093e-01f, 8.831896853053627e-01f, 8.991320235484349e-01f, 9.141540563656075e-01f, 9.282282546151819e-01f, 9.413348145272842e-01f, 9.534619388400459e-01f, 9.646048250501910e-01f, 9.747634827941575e-01f, 9.839435385219192e-01f, 9.921529097154242e-01f, 9.994114730415857e-01f, 1.005746084650236e+00f, 1.011183971347815e+00f, 1.015760373791603e+00f, 1.019515072412387e+00f, 1.022490937034641 e+00f, 1.024736164069697e+00f, 1.026304095700693e+00f, 1.027250978292214e+00f, 1.027634294456205e+00f, 1.027511063644843e+00f, 1.026942795115598e+00f, 1.025991493983836e+00f, 1.024716149969084e+00f, 1.023175976163407e+00f, 1.021427210603284e+00f, 1.019521566634239e+00f, 1.017510118327508e+00f, 1.015439859549357e+00f, 1.013460916839174e+00f, 1.011654901040475e+00f, 1.009366925499550e+00f, 1.007263182132894e+00f, 1.005313192386866e+00f, 1.003508162416449e+00f, 1.001840787319378e+00f, 1.000303927234380e+00f, 9.988898206257559e-01f, 9.975915283480670e-01f, 9.964015284765968e-01f, 9.953133902427869e-01f, 9.943201078053212e-01f, 9.934158959186011e-01f, 9.925943919208190e-01f, 9.918510277326026e-01f, 9.911797988363887e-01f, 9.905771957917731e-01f, 9.900381047643838e-01f, 9.895594394179152e-01f, 9.891371616557014e-01f, 9.887684373604154e-01f, 9.884497924570929e-01f, 9.881790747212391e-01f, 9.879528358230726e-01f, 9.877691368590689e-01f, 9.876249269174586e-01f, 9.875179947346887e-01f, 9.874458127312921e-01f, 9.874056275509585e-01f, 9.873951115886979e-01f, 9.874115368168944e-01f, 9.874524849192456e-01f, 9.875149888347144e-01f, 9.875968894760857e-01f, 9.876951134084213e-01f, 9.878075819424549e-01f, 9.879311998177238e-01f, 9.880640617030884e-01f, 9.882032571565917e-01f, 9.883471084085503e-01f, 9.884926873551375e-01f, 9.886386592120545e-01f, +9.887825578295630e-01f, 9.889230031022089e-01f, 9.890581715933395e-01f, 9.89186767428461 0e-01f, 9.893074965384659e-01f, 9.894196399062921e-01f, 9.895220757174378e-01f, 9.896146331889107e-01f, 9.896970346678272e-01f, 9.897692596535289e-01f, 9.898319269347060e-01f, 9.898852572653667e-01f, 9.899307640365727e-01f, 9.8996931 02025343e-01f, 9.900025692522435e-01f, 9.900321562263099e-01f, 9.900603352632121e-01f, 9.900889812894406e-01f, 9.901206586012907e-01f, 9.901575015155720e-01f, 9.902023946214220e-01f, 9.902575406142213e-01f, 9.903255289051605e-01f, 9.904087914462694e-01f, 9.905096491583045e-01f, 9.906303787150326e-01f, 9.907727108894024e-01f, 9.909387444078919e-01f, 9.911298894709990e-01f, 9.913476318763218e-01f, 9.915928560402563e-01f, 9.918665491182922e-01f, 9.921691315380984e-01f, 9.925010851461232e-01f, 9.928619727154252e-01f, 9.932519181564613e-01f, 9.936700207375173e-01f, 9.941156069136238e-01f, 9.945873147903244e-01f, 9.950837402063278e-01f, 9.956033775539884e-01f, 9.961439922621166e-01f, 9.967034533921340e-01f, 9.972793109558521e-01f, 9.978690858367024e-01f, 9.984697087896268e-01f, 9.990784840729244e-01f, 9.996919011206490e-01f, 1.000308193833526e+00f, 1.000922365901945e+00f, 1.001532636590676e+00f, 1.002135464655177e+00f, 1.002728111386909e+00f, 1.003307449770187e+00f, 1.003870934089686e+00f, 1.004416038098237e+00f, 1.004940548815171 e+00f, 1.005442141810160e+00f, 1.005919224127911 e+00f, 1.006370303149314e+00f, 1.006793927824538e+00f, 1.007189345025525e+00f, 1.007555573455895e+00f, 1.007892674961336e+00f, 1.008200146369426e+00f, 1.008478423284851e+00f, 1.008727884997619e+00f, 1.008949493525753e+00f, 1.009144112734761e+00f, 1.009313224929575e+00f, 1.009458241425143e+00f, 1.009581280555682e+00f, 1.009684090687164e+00f, 1.009768980817384e+00f, 1.009838308708799e+00f, 1.009894548257807e+00f, 1.009940336228694e+00f, 1.009977916643680e+00f, 1.010010230290263e+00f, 1.010039453539107e+00f, 1.010068202038694e+00f, 1.010098388689342e+00f, 1.010132323996401 e+00f, 1.010171656775640e+00f, 1.010218096148412e+00f, 1.010272524848519e+00f, 1.010336490294771e+00f, 1.010410221483215e+00f,
[0204] Un ejemplo numérico de función de formación en ventanas W320, para el tamaño de trama N = 320 se propor ciona aquí (640 muestras):
-3.021153494057143e-04f, -5.867737487939294e-04f, -8.366504004139796e-04f, -1.126635355725494e-03f, -1.470492941694331e-03f, -1.873473391018495e-03f, -2.339292362082021e-03f, -2.872008069419264e-03f, -3.476256385086407e-03f, -4.155963816705528e-03f, -4.914563787665504e-03f, -5.755172503953251e-03f, -6.680623380533122e-03f, -7.693816924650567e-03f, -8.796760749750191e-03f, -9.990503073705982e-03f, -1.127574117138621e-02f, -1.265334152129685e-02f, -1.412438986522702e-02f, -1.568889620430290e-02f, -1.734512089366117e-02f, -1.909097368362797e-02f, -2.092546711168754e-02f, -2.284684792818856e-02f, -2.485207716234951e-02f, -2.693746704328349e-02f, -2.909952486193999e-02f, -3.133504629493832e-02f, -3.363960728361352e-02f, -3.600820974457969e-02f, -3.843601741746971e-02f, -4.091746034850161e-02f, -4.344654894948344e-02f, -4.601786724624048e-02f, -4.862598509282497e-02f, -5.126474204655663e-02f, -5.392644753556616e-02f, -5.660384311081047e-02f, -5.929116747072080e-02f, -6.198268202511926e-02f, -6.467025548071184e-02f, -6.734542216184526e-02f, -7.000099017198280e-02f, -7.263057011354321e-02f, -7.522784961377151e-02f, -7.778525942347714e-02f, -8.029480247839878e-02f, -8.274924535373614e-02f, -8.514125464087215e-02f, -8.746379123238275e-02f, -8.971069341834263e-02f, -9.187564084638347e-02f, -9.395176975347193e-02f, -9.593137735886889e-02f, -9.780843257659243e-02f, -9.957851303827886e-02f, -1.012361165314596e-01f, -1.027741036495644e-01f, -1.041861222641119e-01f, -1.054680247057000e-01f, -1.066160875985523e-01f, -1.076255384835563e-01f, -1.084912299471198e-01f, -1.092087422379003e-01f, -1.097736146613313e-01f, -1.101808861640070e-01f, -1.104271876052675e-01f, -1.105108362290460e-01f, -1.104281465492726e-01f, -1.101739218186236e-01f, -1.097437360338336e-01f, -1.091353125572511e-01f, -1.083467335729228e-01f, -1.073739938306107e-01f, -1.062130155324388e-01f, -1.048606145834788e-01f, -1.033132401525343e-01f, -1.015673163469357e-01f, -9.962005506126154e-02f, -9.746803229469267e-02f, -9.510723623306666e-02f, -9.253303383231506e-02f, -8.974125216128212e-02f, -8.672877689119252e-02f, -8.349213839083708e-02f, -8.002639902061687e-02f, -7.632679536516856e-02f, -7.238806162166744e-02f, -6.820576796149519e-02f, -6.377611429172260e-02f, -5.909386001558149e-02f, -5.415316322402774e-02f, -4.894812724598650e-02f, -4.347347112195197e-02f, -3.772461300253332e-02f, -3.169587609244436e-02f, -2.538179830690266e-02f, -1.877689096555516e-02f, -1.187461378850388e-02f, -4.669099247423082e-03f, 2.844096748870385e-03f, 1.066976124794342e-02f, 1.881355950582949e-02f, 2.728156010437695e-02f, 3.607810469851272e-02f, 4.520702759803914e-02f, 5.467238802204326e-02f, 6.447866054615346e-02f, 7.462862199422061e-02f, 8.512490568723846e-02f, 9.596983987496970e-02f, 1.071650779014335e-01f, 1.187115850305241e-01f, 1.306101067250375e-01f, 1.428596447589721e-01f, 1.554584725339102e-01f, 1.684041609371527e-01f, 1.816947894623263e-01f, 1.953273880886783e-01f, 2.092963206850239e-01f, 2.235945635254679e-01f, 2.382160219461597e-01f, 2.531529721334063e-01f, 2.683961570569586e-01f, 2.839361392493072e-01f, 2.997624255177811e-01f, 3.158619077906196e-01f, 3.322210551086769e-01f, 3.488264676990591e-01f, 3.656640377499646e-01f, 3.827152968157059e-01f, 3.999611859760947e-01f, 4.173843265025887e-01f, 4.349669624916473e-01f, 4.526876397402144e-01f, 4.705242008503956e-01f, 4.884539254831315e-01f, 5.064545550235134e-01f, 5.245006748662190e-01f, 5.425674372882107e-01f, 5.606312044701524e-01f, 5.786672646386708e-01f, 5.966477035050948e-01f, 6.145458904162185e-01f, 6.323361944662236e-01f, 6.499926319211774e-01f, 6.674874032292857e-01f, 6.847932667399612e-01f, 7.018835463513400e-01f, 7.187322544823347e-01f, 7.353128213893310e-01f, 7.516001985652684e-01f, +7.675699252273948e-01f, 7.831974571624924e-01f, 7.984583859818390e-01f, 8.133295347030278e-01f, 8.277892271515950e-01f, 8.418178561101360e-01f, 8.553961300139363e-01f, 8.685068980898102e-01f, 8.811334436653052e-01f, 8.932596784799233e-01f, 9.048748835980528e-01f, 9.159657608120536e-01f, 9.265215299450000e-01f, 9.365339988633418e-01f, 9.459977028429117e-01f, 9.549088408436811e-01f, 9.632658122557368e-01f, 9.710688896122810e-01f, 9.783204156360773e-01f, 9.850226760127131e-01f, 9.911792082081333e-01f, 9.967989944502682e-01f, 1.001894024615659e+00f, 1.006474342231823e+00f, 1.010552057109195e+00f, 1.014142538208007e+00f, 1.017262593268930e+00f, 1.019928842669923e+00f, 1.022159867011177e+00f, 1.023976320927187e+00f, 1.025400734608122e+00f, 1.026455340400072e+00f, 1.027164510654160e+00f, 1.027552729180790e+00f, 1.027644462380432e+00f, 1.027463246660797e+00f, 1.027035903410657e+00f, 1.026389068000259e+00f, 1.025548201799728e+00f, 1.024537134749709e+00f, 1.023380803775376e+00f, 1.022103695693341e+00f, 1.020728359657958e+00f, 1.019275334687329e+00f, 1.017765178792830e+00f, 1.016217355867531e+00f, 1.014665311686846e+00f, 1.013249071090664e+00f, 1.011948006992127e+00f, 1.010189090179223e+00f, 1.008557961167850e+00f, 1.007011287608451e+00f, 1.005548764575910e+00f, 1.004168417268956e+00f, 1.002867268893035e+00f, 1.001641769115897e+00f, 1.000489068954641e+00f, 9.994060799749374e-01f, 9.983898865406841e-01f, 9.974370849972721e-01f, 9.965444836911705e-01f, 9.957098545943852e-01f, 9.949302413030897e-01f, 9.942024045863540e-01f, 9.935241604969254e-01f, 9.928930430130044e-01f, 9.923068103443909e-01f, 9.917633778190438e-01f, 9.912597642374404e-01f, 9.907954498484041e-01f, 9.903677893656558e-01f, 9.899751611066148e-01f, 9.896160337369861e-01f, 9.892890160408989e-01f, 9.889928511129679e-01f, 9.887260333430423e-01f, 9.884868721088945e-01f, 9.882751039537586e-01f, 9.880892168751595e-01f, 9.879277114724612e-01f, 9.877898261218510e-01f, 9.876743442038471e-01f, 9.875807496078497e-01f, 9.875072021876561e-01f, 9.874529447589979e-01f, 9.874169741527905e-01f, 9.873984685207834e-01f, 9.873958301311858e-01f, 9.874080027710336e-01f, 9.874343401290739e-01f, 9.874736235387018e-01f, 9.875243137719285e-01f, 9.875856201221135e-01f, 9.876563785063032e-01f, 9.877358921155149e-01f, 9.878225576787804e-01f, 9.879150968481590e-01f, 9.880132731565830e-01f, 9.881156946084619e-01f, 9.882211314188272e-01f, 9.883289032519310e-01f, 9.884378310018685e-01f, 9.885476787868710e-01f, 9.886568414746639e-01f, 9.887645868459630e-01f, 9.888708540445242e-01f, 9.889744320992592e-01f, 9.890747269455915e-01f, 9.891710038703801e-01f, 9.892631024032380e-01f, 9.893507219573624e-01f, 9.894330645494204e-01f, 9.895096919388534e-01f, 9.895810813422480e-01f, 9.896467469067676e-01f, 9.897067365020641e-01f, 9.897606930400666e-01f, 9.898094478563998e-01f, 9.898530133261707e-01f, 9.898914705684924e-01f, 9.899254194103574e-01f, 9.899554202030650e-01f, 9.899824494486951e-01f, 9.900065116928948e-01f, 9.900284805353695e-01f, 9.900497484789281e-01f, 9.900709561632662e-01f, 9.900928358611601e-01f, 9.901163920607219e-01f, 9.901427479709606e-01f, 9.901734275350572e-01f, 9.902087332329851e-01f, 9.902498637985275e-01f, 9.902983686695558e-01f, 9.903548501470234e-01f, 9.904205084933333e-01f, 9.904959297726740e-01f, 9.905825150202904e-01f, 9.906812569810133e-01f, 9.907922087340426e-01f, 9.909165464981378e-01f, 9.910550740962871e-01f, 9.912084614290896e-01f, 9.913768610980639e-01f, 9.915605826937839e-01f, 9.917604214872976e-01f, 9.919767175562684e-01f, 9.922091101818779e-01f, 9.924579135466506e-01f, 9.927231225056266e-01f, 9.930049538427406e-01f, 9.933027281437943e-01f, 9.936161084869942e-01f, 9.939453714404443e-01f, 9.942895145656371e-01f, 9.946481676207727e-01f, 9.950203031067961e-01f, 9.954058173659507e-01f, 9.958038713694317e-01f, 9.962130271017117e-01f, 9.966324689957675e-01f, 9.970615306490058e-01f, 9.974990583293081e-01f, 9.979437430375855e-01f, 9.983940572002874e-01f, 9.988493116887893e-01f, 9.993083430214909e-01f, 9.997689221333534e-01f, 1.000231131275969e+00f, 1.000692135698996e+00f, 1.001152013920163e+00f, 1.001608526000461e+00f, 1.002060493867275e+00f, 1.002507212061815e+00f, 1.002947129400411e+00f, 1.003378909587027e+00f, 1.003801368578070e+00f, 1.004213810320699e+00f, 1.004615386562846e+00f, 1.005004618375781 e+00f, 1.005380628601598e+00f, 1.005743282364652e+00f, 1.006091510392348e+00f, 1.006424907424988e+00f, 1.006742427727669e+00f, 1.007044321511378e+00f, 1.007330218597112e+00f, 1.007599401798709e+00f, 1.007852064386603e+00f, 1.008088176165563e+00f, 1.008308033204578e+00f, 1.008511247273756e+00f, 1.008698144207627e+00f, 1.008869515256392e+00f, 1.009025659761512e+00f, 1.009166718967367e+00f, 1.009293362609020e+00f, 1.009406398832440e+00f, 1.009507017171120e+00f, 1.009595264293017e+00f, 1.009672145744679e+00f, 1.009739084785160e+00f, 1.009796675060142e+00f, 1.009846137382005e+00f, 1.009888083631667e+00f, 1.009924092276850e+00f, 1.009955384765721 e+00f, 1.009982268770147e+00f, 1.010006298177305e+00f, 1.010028618428735e+00f, 1.010050254076988e+00f, 1.010071952131355e+00f, 1.010094366238073e+00f, 1.010118917317053e+00f, 1.010146497096682e+00f, 1.010177110711677e+00f, 1.010211755260102e+00f, 1.010251003469427e+00f, 1.010295468653759e+00f, 1.010345234996637e+00f, 1.010400316698172e+00f, 1.010461564316351 e+00f, 1.010528615445659e+00f, 1.010601521285347e+00f, 1.010679788081867e+00f, 1.010763905869062e+00f, 1.010853429760676e+00f, 1.010947547074519e+00f, 1.011045953108263e+00f, 1.011148486293359e+00f, 1.011254397791134e+00f, 1.011363082075863e+00f, 1.011473302008831e+00f, 1.011584996312149e+00f, 1.011697416504599e+00f, 1.011808919793469e+00f, 1.011919264025716e+00f, 1.012027240794153e+00f, 1.012132151631041e+00f, 1.012232734564333e+00f, 1.012327560477901e+00f, 1.012416383754384e+00f, 1.012497890726292e+00f, 1.012570434021054e+00f, 1.012633295255708e+00f, 1.012685277016726e+00f, 1.012725564992284e+00f, 1.012752577651415e+00f, 1.012765062889864e+00f, 1.012762356719162e+00f, 1.012743376077777e+00f, 1.012706484200181e+00f, 1.012650842226435e+00f, 1.012575427778520e+00f, 1.012479473490919e+00f, 1.012361105121003e+00f, 1.012219809594718e+00f, 1.012054359992419e+00f, 1.011864000215460e+00f, 1.011647223869087e+00f, + 1.011402518267713e+00f, 1.011129654652857e+00f, 1.010826951260377e+00f, 1.010492924436361e+00f, 1.010126353960416e+00f, 1.009725892479312e+00f, 1.009290060983833e+00f, 1.008817301052548e+00f, 1.008305027555130e+00f, 1.007752833675443e+00f, 1.007157827358150e+00f, 1.006518049344503e+00f, 1.005831403532018e+00f, 1.005095592119373e+00f, 1,004308630055050e+00f, 1.003467498305776e+00f, 1.002569500413888e+00f, 1.001612710105563e+00f, 1.000594272975683e+00f, 9.995111701168786e-01f, 9.983609218719522e-01f, 9.971409288327860e-01f, 9.958488863050556e-01f, 9.944818543153893e-01f, 9.930375282832211e-01f, 9.915146560759479e-01f, 9.899136802423638e-01f, 9.881930623810997e-01f, 9.859422591203311e-01f, 9.835667898378924e-01f, 9.811423034808365e-01f, 9.785214441250228e-01f, 9.756636036109838e-01f, 9.725453442532574e-01f, 9.691456634185092e-01f, 9.654406178310209e-01f, 9.614043615076308e-01f, 9.570113065179300e-01f, 9.522367669696690e-01f, 9.470548839544214e-01f, 9.414403740008491e-01f, 9.353691612846549e-01f, 9.288190093977164e-01f, 9.217662887169115e-01f, 9.141896283466009e-01f, 9.060694681113471e-01f, 8.973891675497357e-01f, 8.881332000806269e-01f, 8.782893885841422e-01f, 8.678469565343039e-01f, 8.567970644671067e-01f, 8.451334654019180e-01f, 8.328542805780399e-01f, 8.199594783897041e-01f, 8.064511006873497e-01f, 7.923346478686025e-01f, 7.776204488292163e-01f, 7.623206183595970e-01f, 7.464486491227057e-01f, 7.300205729992958e-01f, 7.130567383226717e-01f, 6.955805444755916e-01f, 6.776173229836567e-01f, 6.591955305148172e-01f, 6.403486426892321e-01f, 6.211072197441818e-01f, 6.015049275244730e-01f, 5.815787608870452e-01f, 5.613674511156324e-01f, 5.409188627354076e-01f, 5.202736834971303e-01f, 4.994780733459294e-01f, 4.785774177949064e-01f, 4.576172599874928e-01f, 4.366490208265804e-01f, 4.157221460415995e-01f, 3.948856590950757e-01f, 3.741903189229770e-01f, 3.536868899553974e-01f, 3.334260017756462e-01f, 3.134586473252229e-01f, 2.938337904395871e-01f, 2.745992637590817e-01f, 2.558030636168172e-01f, 2.374902188466697e-01f, 2.197036032185785e-01f, 2.024855415115456e-01f, 1.858749915117319e-01f, 1.699067802117410e-01f, 1.546132267478873e-01f, 1.400238206749695e-01f, 1.261637395672913e-01f, 1.130534434072719e-01f, 1.007084973747940e-01f, 8.914024389873081e-02f, 7.835612100141792e-02f, 6.835821233920988e-02f, 5.914211536028976e-02f, 5.069893012340832e-02f, 4.301717763585550e-02f, 3.608020726673359e-02f, 2.986316337017630e-02f, 2.433722657129812e-02f, 1.947675241971700e-02f, 1.525710171255895e-02f, 1.163787492636240e-02f, 8.433087782643718e-03f, 4.449668997344735e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f
[0205] Un ejemplo numérico de función de formación en ventanas W480, para el tamaño de trama N = 480 se proporciona aquí (960 muestras):
-2.353032150516754e-04f, -4.619898752628163e-04f, -6.262931535610879e-04f, -7.929180432976445e-04f, -9.747166718929050e-04f, -1.180256894474562e-03f, -1.409209039594871e-03f, -1.664473096973725e-03f, -1.946591608170231e-03f, -2.257081732588478e-03f, -2.597106916737789e-03f, -2.967607624839524e-03f, -3.370454877988472e-03f, -3.806285163352241e-03f, -4.276873767639064e-03f, -4.782469904501813e-03f, -5.324608721716763e-03f, - 5.903403814095400e-03f, -6.520419726599805e-03f, 7.175885277771099e-03f, -7.871422820642307e-03f, - 8.606586039759667e-03f, ■9.382480860899108e-03f, 1.019827182163307e-02f, -1.105520547739066e-02f, - 1.195270300743193e-02f, ■1.289205910303846e-02f, ■1.387263484323160e-02f, -1.489528159506296e-02f, - 1.595856621933800e-02f, -1.706288556735433e-02f, 1.820666399965468e-02f, -1.939065975232718e-02f, - 2.061355417582714e-02f, -2.187570925786862e-02f, 2.317526315266411e-02f, -2.451227449041489e-02f, - 2.588471937157619e-02f, -2.729263737090799e-02f, 2.873390902713615e-02f, -3.020862738245264e-02f, - 3.171440372994384e-02f, -3.325098858986303e-02f, 3.481597793538342e-02f, -3.640892406933019e-02f, - 3.802742318209150e-02f, -3.967067992672979e-02f, 4.133575417353826e-02f, -4.302203371734278e-02f, - 4.472698045914417e-02f, -4.645022292934329e-02f, 4.818891490266687e-02f, -4.994225863256500e-02f, - 5.170690802826666e-02f, -5.348162036097223e-02f, 5.526334794593565e-02f, -5.705123152423822e-02f, - 5.884271749745559e-02f, -6.063717235243996e-02f, 6.243104027829089e-02f, -6.422303545004304e-02f, - 6.600961519440657e-02f, -6.778962269634495e-02f, 6.955996868581379e-02f, -7.131966266443390e-02f, - 7.306581273272733e-02f, -7.479758913001458e-02f, 7.651178225890490e-02f, -7.820711420768856e-02f, - 7.988010693411644e-02f, -8.152964005319532e-02f, 8.315237353264004e-02f, -8.474728946770714e-02f, - 8.631137544905677e-02f, -8.784374452959058e-02f, 8.934164364321417e-02f, -9.080411291245728e-02f, - 9.222795761428432e-02f, -9.361232867223340e-02f, 9.495377758870335e-02f, 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9.951746430061121e-01f, 9.942466438407230e-01f, 9.932837131068657e-01f, 9.922861082472264e-01f, 9.912523092989319e-01f, 9.901827419790691e-01f, 9.890757868707590e-01f, 9.879313024174022e-01f, 9.863553220272523e-01f, 9.847362453480265e-01f, 9.831750948772566e-01f, 9.815583336011345e-01f, 9.798613526271561e-01f, 9.780617486993630e-01f, 9.761574317374303e-01f, 9.741378617337759e-01f, 9.719990112065752e-01f, 9.697327413658168e-01f, 9.673331975559332e-01f, 9.647915124057732e-01f, 9.621011497566145e-01f, 9.592539757044516e-01f, 9.562427177295731e-01f, 9.530600909726344e-01f, 9.496984081652284e-01f, 9.461498120176854e-01f, 9.424071613625743e-01f, 9.384634163826711e-01f, 9.343112966094085e-01f, 9.299449872197452e-01f, 9.253567968750328e-01f, 9.205404627076625e-01f, 9.154896280575360e-01f, 9.101986790930605e-01f, 9.046620597741508e-01f, 8.988755194372424e-01f, 8.928338316495705e-01f, 8.865337190368053e-01f, 8.799712722567934e-01f, 8.731437835983047e-01f, 8.660476534563131e-01f, 8.586812520174252e-01f, 8.510420440685049e-01f, 8.431297226886574e-01f, 8.349435141989714e-01f, 8.264839911291133e-01f, 8.177505366573690e-01f, 8.087449817124315e-01f, 7.994681492797084e-01f, 7.899235162194718e-01f, 7.801137731566502e-01f, 7.700431275216928e-01f, 7.597145736971065e-01f, 7.491330971820804e-01f, 7.383028603058783e-01f, 7.272298755824693e-01f, 7.159201919962611e-01f, 7.043814340356083e-01f, 6.926196927377140e-01f, 6.806438831866077e-01f, 6.684616478236647e-01f, 6.560830137986515e-01f, 6.435179268559957e-01f, 6.307755329382612e-01f, 6.178641647786525e-01f, 6.047954625702541e-01f, 5.915799587176216e-01f, 5.782289366005894e-01f, 5.647535885752191e-01f, 5.511703155400274e-01f, 5.374905090437071e-01f, 5.237263500445715e-01f, 5.098915423728255e-01f, 4.960008074926423e-01f, 4.820662943337458e-01f, 4.681017110048007e-01f, 4.541216995958746e-01f, 4.401421815729068e-01f, 4.261772971493010e-01f, 4.122417888542512e-01f, 3.983499612526493e-01f, 3.845172335531009e-01f, 3.707583717376236e-01f, 3.570886786795506e-01f, 3.435228672445627e-01f, 3.300763764703638e-01f, 3.167640325043893e-01f, 3.036004651973109e-01f, 2.905996158436682e-01f, 2.777758503744847e-01f, 2.651434678028531e-01f, 2.527161881181577e-01f, 2.405069849650012e-01f, 2.285283969438072e-01f, 2.167933432162879e-01f, 2.053139897833021e-01f, 1.941021906320988e-01f, 1.831680872008943e-01f, 1.725221947208913e-01f, 1.621735416384834e-01f, 1.521320683467849e-01f, 1.424052801149985e-01f, 1.330015240938615e-01f, 1.239260664828526e-01f, 1.151858295527293e-01f, 1.067840430193724e-01f, 9.872637505002878e-02f, 9.101379000888035e-02f, 8.365057236623055e-02f, 7.663508305536153e-02f, 6.997033405748826e-02f, 6.365188111381365e-02f, 5.768176015814392e-02f, 5.205244216987966e-02f, 4.676538412257621e-02f, 4.180950541438362e-02f, 3.718640251368464e-02f, 3.288072750732215e-02f, 2.889548499582958e-02f, 2.520980565928884e-02f, 2.183057564646272e-02f, 1.872896194002638e-02f, 1.592127815153420e-02f, 1.336381425803020e-02f, 1.108558877807282e-02f, 8.943474189364638e-03f, 6.758124889697787e-03f, 3.504438130619497e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, +0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f 0.000000000000000e+00f, 0.000000000000000e+00f
[0206] Un ejemplo numérico de función de formación en ventanas wg60, para el tamaño de trama N = 960 se proporciona aquí (1920 muestras):
-1.596869453315999e-04, -3.021153494057143e-04 -4.142323860121641e-04, -5.058484031439142e-04 -5.867737487939294e-04, -6.666034929771656e-04 -7.499813122143762e-04, -8.366504004139794e-04 -9.273096237893370e-04, -1.023773491532728e-03 -1.126635355725494e-03, -1.235247794937702e-03 -1.349627853510606e-03, -1.470492941694331e-03 -1.598145399394582e-03, -1.732450700747454e-03 -1.873473391018495e-03, -2.021493133113876e-03 -2.176721793926887e-03, -2.339292362082021e-03 -2.509298051958086e-03, -2.686801873698675e-03 -2.872008069419264e-03, -3.065254982136409e-03 -3.266686736002951e-03, -3.476256385086407e-03 -3.694123506258334e-03, -3.920651988943251e-03 -4.155963816705528e-03, -4.399940204176431e-03 -4.652692827862344e-03, -4.914563787665504e-03 -5.185653529531935e-03, -5.465821495567872e-03 -5.755172503953251e-03, -6.054056765330685e-03 -6.362583863449497e-03, -6.680623380533122e-03 -7.008304674718039e-03, -7.346013465075499e-03 -7.693816924650567e-03, -8.051465262788033e-03 -8.419001443263380e-03, -8.796760749750191e-03 -9.184751507972289e-03, -9.582657230262597e-03 -9.990503073705982e-03, -1.040865597419619e-02 -1.083716113754551e-02, -1.127574117138621e-02 -1.172444049589271e-02, -1.218362542421523e-02 -1.265334152129685e-02, -1.313331245904876e-02 -1.362355747138776e-02, -1.412438986522702e-02 -1.463576680723352e-02, -1.515729094197161e-02 -1.568889620430290e-02, -1.623084814367250e-02 -1.678306524600559e-02, -1.734512089366117e-02 -1.791696516251699e-02, -1.849892453107246e-02 -1.909097368362797e-02, -1.969273308274951e-02 -2.030414376031160e-02, -2.092546711168754e-02 -2.155660557689242e-02, -2.219710359529686e-02 -2.284684792818856e-02, -2.350606779320675e-02 -2.417463749934085e-02, -2.485207716234951e-02 -2.553826580898371e-02, -2.623344061522424e-02 -2.693746704328349e-02, -2.764983997782559e-02 -2.837043858580717e-02, -2.909952486193998e-02 -2.983695676902939e-02, -3.058218787751172e-02 -3.133504629493832e-02, - 3.209573641742117e-02, -3.286409853195186e-02, -3.363960728361352e-02 -3.442207835192332e-02, - 3.521166997276568e-02, -3.600820974457969e-02, -3.681119317395579e-02 -3.762042487257546e-02, - 3.843601741746971e-02, -3.925772507976759e-02, -4.008494689009130e-02 -4.091746034850161e-02, - 4.175542154425013e-02, -4.259863408038441e-02, -4.344654894948344e-02 -4.429899287523113e-02, - 4.515616616948602e-02, -4.601786724624048e-02, -4.688349274164030e-02 -4.775281564045485e-02, - 4.862598509282498e-02, -4.950274425624717e-02, -5.038242975874127e-02 -5.126474204655663e-02, - 5.214974857230398e-02, -5.303718358615044e-02, -5.392644753556616e-02 -5.481729406855359e-02, - 5.570983057565210e-02, -5.660384311081047e-02, -5.749879655200370e-02 -5.839451321393058e-02, - ■5.929116747072080e-02, -6.018848884279070e-02, -6.108576415855094e-02 -6.198268202511926e-02, - 6.287933502598060e-02, -6.377542359879805e-02, -6.467025548071184e-02 -6.556352962710620e-02, - 6.645533804325808e-02, -6.734542216184526e-02, -6.823317113969737e-02 -6.911832800881393e-02, - 7.000099017198280e-02, -7.088091415536939e-02, -7.175751581450866e-02 -7.263057011354321e-02, - 7.350020923324756e-02, -7.436618116832702e-02, -7.522784961377151e-02 -7.608493286734087e-02, - 7.693750413779520e-02, -7.778525942347714e-02, -7.862751920094575e-02 -7.946399769633587e-02, - 8.029480247839879e-02, -8.111965623403654e-02, -8.193789640255647e-02 -8.274924535373614e-02, - 8.355381170261278e-02, -8.435134905678848e-02, -8.514125464087215e-02 -8.592328028689659e-02, - 8.669753354886602e-02, -8.746379123238275e-02, -8.822149831804039e-02 -8.897043074644968e-02, - 8.971069341834263e-02, -9.044201341183719e-02, -9.116374329727489e-02 -9.187564084638347e-02, - 9.257786640497777e-02, -9.327014538321736e-02, -9.395176975347193e-02 -9.462246851310178e-02, - 9.528240981433814e-02, -9.593137735886889e-02, -9.656876884228789e-02 -9.719438533739366e-02, - 9.780843257659243e-02, -9.841075978146442e-02, -9.900085534600200e-02 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3.673320150150139e-01 , 3.604969483256886e-01 , 3.536868899553974e-01 3.469037339648918e-01 3.401494735467201e-01 , 3.334260017756462e-01 , 3.267351352184045e-01 3.200787300572631e-01 3.134586473252229e-01 , 3.068766522215559e-01 , 3.003344428572218e-01 2.938337904395881e-01 2.873765136803315e-01 , 2.809644064498411e-01 , 2.745992637590826e-01 2.682828578001429e-01 2.620169058204753e-01 , 2.558030636168179e-01 , 2.496429506725780e-01 2.435381581076193e-01 2.374902188466703e-01 , 2.315007158769866e-01 , 2.255713139320687e-01 2.197036032185791e-01 2.138990608950040e-01 , 2.081591884177564e-01 , 2.024855415115456e-01 1.968794982265323e-01 1.913422230760984e-01 , 1.858749915117319e-01 , 1.804792270036454e-01 1.751561592043750e-01 1.699067802117410e-01 , 1.647322739698192e-01 , 1.596340539111631e-01 1.546132267478876e-01 1.496705434426226e-01, 1.448069879076800e-01, 1.400238206749698e-01, 1.353218971490514e-01 1.307016182576054e-01 , 1.261637395672916e-01 , 1.217094187032866e-01 1.173392980385558e-01 1.130534434072722e-01 , 1.088524061173192e-01 , 1.047372831131808e-01 1.007084973747942e-01 9.676572618933918e-02 , 9.290929444691418e-02 , 8.914024389873081e-02 8.545874375771015e-02 8.186400751918757e-02 , 7.835612100141792e-02 , 7.493612463933132e-02 7.160392900131578e-02 6.835821233920988e-02 , 6.519882821193619e-02 , 6.212691236769909e-02 5.914211536028985e-02 5.624247476796568e-02 , 5.342762364238927e-02 , 5.069893012340838e-02 4.805577285587748e-02 4.549537570011979e-02 , 4.301717763585556e-02 , 4.062301532941800e-02 3.831198264259714e-02 3.608020726673365e-02 , 3.392698736873631e-02 , 3.185504779821543e-02 2.986316337017634e-02 2.794584821783607e-02 , 2.610239043507366e-02 , 2.433722657129812e-02 2.264871565562373e-02 2.102867478775550e-02 , 1.947675241971700e-02 , 1.800101670620712e-02 1.659903330901047e-02 1.525710171255895e-02 , 1.397610119023076e-02 , 1.277238121584596e-02 1.163787492636242e-02 1.053809096662833e-02 , 9.464262017505555e-03 , 8.433087782643726e-03 7.364501936162659e-03 6.073847663871269e-03, , 4.449668997344740e-03 , 2.485333612762431e-03 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00, 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0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
7.2 Ejemplos asociados a las Figuras 26 a 30
[0207] Un ejemplo numérico de función de formación en ventanas W40, para el tamaño de trama N=40 se pro porciona aquí por 80 entradas para n = 0... 2N-1. Tal y como se explicó más arriba, los últimos valores pueden ser 0. 9.959086585790517e-04, 3.819056787237678e-03, 9.540832613229890e-03, 1.921659800166160e-02, 3.382719081038548e-02, 5.424831667522354e-02, 8.12077766877561 0e-02, 1.152171887125930e-01, 1.564942331034909e-01, 2.049363422022628e-01, 2.601166575816199e-01, 3.212814164616093e-01, 3.873472997948746e-01, 4.569497078592333e-01, 5.285192958868393e-01, 6.003522489375573e-01, 6.706896380227332e-01, 7.378044458510402e-01, 8.000925313431716e-01, 8.561409184410547e-01, 9.048272294524792e-01, 9.453685031730190e-01, 9.773507430600533e-01, 1.000800872826561e+00, 1.016171590112097e+00, 1.024315247630982e+00, 1.026415431432931e+00, 1.023858366571912e+00, 1.018135705524407e+00, 1.010794822557756e+00, 1.003406509762925e+00, 9.967831265986109e-01, 9.920995520917141e-01, 9.892206942816891e-01, 9.879658322200813e-01, 9.881273531631907e-01, 9.894805541465801e-01, 9.917849916000535e-01, 9.947847580943504e-01, 9.982119669301160e-01, 1.001791235858836e+00, 1.005242583245485e+00, 1.008283053756130e+00, 1.010631281038659e+00, 1.012015300253356e+00, 1.012180753005270e+00, 1.010896765282633e+00, 1.007963362035220e+00, 1.003227255072391e+00, 9.966050551498514e-01, 9.868284225039941e-01, 9.731250287581631e-01, 9.540636479502398e-01, 9.283864275822276e-01, 8.950916858157935e-01, 8.534769362643825e-01, 8.032090930429980e-01, 7.444735201251689e-01, 6.780787033699449e-01, 6.053970453856138e-01, 5.282077505750667e-01, 4.486552956056635e-01, 3.691875990296312e-01, 2.924566408966777e-01, 2.210718537110463e-01, 1.573148583944309e-01, 1.030525757797768e-01, 5.982732244758054e-02, 2.871831923385133e-02, 9.683884928956490e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
[0208] Un ejemplo numérico de función de formación en ventanas W80, para el tamaño de trama N=80 se pro porciona aquí por 160 entradas para n = 0 . 2N-1. Tal y como se explicó más arriba, los últimos valores pueden ser 0. 6.143388180964179e-04, 1.489582832987000e-03,
+2.884104959764029e-03, 4.934298832466617e-03, 7.779130464154915e-03, 1.154910606525086e-02, 1.637155619860352e-02, 2.237116158648752e-02, 2.966159685753317e-02, 3.835663329277230e-02, 4.855610986150206e-02, 6.035055738891727e-02, 7.382288203064732e-02, 8.903563687211119e-02, 1.060356225286319e-01, 1.248534855777947e-01, 1.454931890869180e-01, 1.679435556337752e-01, 1.921728622634411e-01, 2.181238261985594e-01, 2.457259744642953e-01, 2.748839432649996e-01, 3.054824712370942e-01, 3.373873799614014e-01, 3.704415932452488e-01, 4.044749630814483e-01, 4.393004362003260e-01, 4.747225454237193e-01, 5.105341492548225e-01, 5.465201916422433e-01, 5.824658100332457e-01, 6.181452662624718e-01, 6.533411462740817e-01, 6.878367295965062e-01, 7.214176027060971e-01, 7.538887973483771e-01, 7.850546571907628e-01, 8.147397447696774e-01, 8.427819363777799e-01, 8.690376742017057e-01, 8.933935477349644e-01, 9.157483563218768e-01, 9.360270196617569e-01, 9.541731142261065e-01, 9.701635474343885e-01, 9.840036439809510e-01, 9.957199420334376e-01, 1.005374268639838e+00, 1.013046655758663e+00, 1.018843380560658e+00, 1.022896948293643e+00, 1.025355286710874e+00, 1.026382881625701e+00, 1.026155530733488e+00, 1.024853974580724e+00, 1.022664602721801e+00, 1.019779396547454e+00, 1.016391686789653e+00, 1.012697033320358e+00, 1.008885191761748e+00, 1.005378742804807e+00, 1.001563778373068e+00, 9.982531564931281e-01, 9.954346644968789e-01, 9.930950268060122e-01, 9.912170911359961e-01, 9.897805192546195e-01, 9.887624937408933e-01, 9.881383235740961e-01, 9.878819413827574e-01, 9.879662130250981e-01, 9.883630508181326e-01, 9.890434070785485e-01, 9.899772316163624e-01, 9.911334564321237e-01, 9.924800441092685e-01, 9.939841207305906e-01, 9.956121471675398e-01, 9.973300590248015e-01, 9.991033633647473e-01, 1.000897441314013e+00, 1.002677088643863e+00, 1.004407190937699e+00, 1.006052289109999e+00, 1.007576934100958e+00, 1.008945862447015e+00, 1.010124241309341e+00, 1.011077969726137e+00, 1.011773962181442e+00, 1.012180362866919e+00, 1.012266707295288e+00, 1.012004064757857e+00, 1.011365223023975e+00, 1.010324996851905e+00, 1.008860731864438e+00, 1.006952983357691e+00, 1.004586273379809e+00, 1.001749900308864e+00, 9.984386632116344e-01, 9.946500332901397e-01, 9.895756853352172e-01, 9.838303127859196e-01, 9.769999155793757e-01, 9.689141159310996e-01, 9.594038121639412e-01, 9.483086322505029e-01, 9.354860218216989e-01, 9.208101305030523e-01, 9.041732260327581e-01, 8.854882249661838e-01, 8.646864947605046e-01, 8.417237467711145e-01, 8.165875713256009e-01, 7.892986353718001e-01, 7.599171886893816e-01, 7.285474515411827e-01, 6.953282935906302e-01, 6.604334017809461e-01, 6.240661431421666e-01, 5.864461424698465e-01, 5.478160663871147e-01, 5.084499758302218e-01, +4.686361426418982e-01, 4.286789889246253e-01, 3.889032719013045e-01, 3.496431418636314e-01, 3.112360816586544e-01, 2.740128472224535e-01, 2.382847225401666e-01, 2.043379825955252e-01, 1.724305860483632e-01, 1.427939789949265e-01, 1.156385879569741e-01, 9.115821766571995e-02, 6.952749039054593e-02, 5.088975408628225e-02, 3.533430192568954e-02, 2.286680405144430e-02, 1.
3380050 16725895e-02, 6.640506529168652e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
[0209] Un ejemplo numérico de función de formación en ventanas W120, para el tamaño de trama N=120 se proporciona aquí por 240 entradas para n = 0... 2N-1. Tal y como se explicó más arriba, los últimos valores pueden ser 0.
+5.087227626168386e-04, 9.959086585790517e-04, 1.682208006328800e-03, 2.609697259047744e-03, 3.819056787237678e-03, 5.349319592933909e-03, 7.243906383895192e-03, 9.540832613229890e-03, 1.227637642543709e-02, 1.548950238899404e-02, 1.921659800166160e-02, 2.349369619441617e-02, 2.835199581667961e-02, 3.382719081038548e-02, 3.994939538719628e-02, 4.674775238543380e-02, 5.424831667522354e-02, 6.247770776443612e-02, 7.145835917501348e-02, 8.120777668775610e-02, 9.174400412319896e-02, 1.030764959637497e-01, 1.152171887125930e-01, 1.281665713944242e-01, 1.419264381068653e-01, 1.564942331034909e-01, 1.718593189799504e-01, 1.880134254543744e-01, 2.049363422022628e-01, 2.226123055761096e-01, 2.410151242797736e-01, 2.601166575816199e-01, 2.798871008989962e-01, 3.002880135563586e-01, 3.212814164616093e-01, 3.428208463088390e-01, 3.648596557863134e-01, 3.873472997948746e-01, 4.102294951869188e-01, 4.334494534591082e-01, 4.569497078592333e-01, 4.806696403251166e-01, 5.045473815014847e-01, 5.285192958868393e-01, 5.525196099932443e-01, 5.764872452085427e-01, 6.003522489375573e-01, 6.240509872809882e-01, 6.475182586093196e-01, 6.706896380227332e-01, 6.935029068990036e-01, 7.158927516396895e-01, 7.378044458510402e-01, 7.591787241845952e-01, 7.799586608897265e-01, 8.000925313431716e-01, 8.195318652294690e-01, 8.382288957404715e-01, 8.561409184410547e-01, 8.732316951214179e-01, 8.894702022170831e-01, 9.048272294524792e-01, 9.192736375782965e-01, 9.327940405054362e-01, 9.453685031730190e-01, 9.569883933538136e-01, 9.676486424195593e-01, 9.773507430600533e-01, 9.861027831072527e-01, 9.939122412655677e-01, 1.000800872826561e+00, 1.006787811971719e+00, 1.011901269172423e+00,+1.016171590112097e+00 , 1.019636414864842e+00, 1.022336613864005e+00, 1.024315247630982e+00, 1.025621299895396e+00 , 1.026303439275662e+00, 1.026415431432931e+00, 1.026007933174836e+00, 1.025137435167917e+00 , 1.023858366571912e+00, 1.022226936424625e+00, 1.020300550334848e+00,+1.018135705524407e+00 , 1.015792146756340e+00, 1.013325966774524e+00, 1.010794822557756e+00, 1.008265131568879e+00 , 1.006046874304407e+00, 1.003406509762925e+00, 1.000977398831985e+00, 9.987704535700208e-01, 9.967831265986109e-01, 9.950118905889862e-01, 9.934523971504882e-01, 9.920995520917141e-01, 9.909475998606236e-01, 9.899902426925508e-01, 9.892206942816891e-01, 9.886318043013834e-01, 9.882160904669929e-01, 9.879658322200813e-01, 9.878730767519871e-01, 9.879296932443894e-01, 9.881273531631907e-01, 9.884575535474619e-01, 9.889115869213529e-01, 9.894805541465801e-01, 9.901553455166457e-01, 9.909266562913843e-01, 9.917849916000535e-01, 9.927206838643636e-01, 9.937239208721489e-01, 9.947847580943504e-01, 9.958931493776203e-01, 9.970389567617592e-01, 9.982119669301160e-01, 9.994020338838508e-01, 1.000598323893564e+00,+1.001791235858836e+00 , 1.002969837054169e+00, 1.004123786397111e+00, 1.005242583245485e+00, 1.006315717067918e+00 , 1.007332693127034e+00, 1.008283053756130e+00, 1.009156423082384e+00, 1.009942535308151e+00 , 1.010631281038659e+00, 1.011212744622770e+00, 1.011677230257499e+00,+1.012015300253356e+00 , 1.012217779097186e+00, 1.012275790821109e+00, 1.012180753005270e+00,+1.011924425888915e+00 , 1.011498917644724e+00, 1.010896765282633e+00, 1.010110965619444e+00, 1.009135094671655e+00 , 1.007963362035220e+00, 1.006590756505588e+00, 1.005013115379014e+00,+1.003227255072391e+00 , 1.001231060075500e+00, 9.990235555436858e-01, 9.966050551498514e-01, 9.939894706113089e-01, 9.904539200261149e-01, 9.868284225039941e-01, 9.827716736909488e-01, 9.782206672373213e-01, 9.731250287581631e-01, 9.674323528812744e-01, 9.610947043524248e-01, 9.540636479502398e-01, 9.462952991190324e-01, 9.377489107516087e-01, 9.283864275822276e-01, 9.181762606422500e-01, 9.070861558801854e-01, 8.950916858157935e-01, 8.821696237804294e-01, 8.683025287048570e-01, 8.534769362643825e-01, 8.376852006833730e-01, 8.209275259764013e-01, 8.032090930429980e-01, 7.845450482523652e-01, 7.649554851899686e-01, 7.444735201251689e-01, 7.231348066419057e-01, 7.009860555207412e-01, 6.780787033699450e-01, 6.544686506489734e-01, 6.302212149502727e-01, 6.053970453856138e-01, 5.800715766089168e-01, 5.543129276657669e-01, 5.282077505750727e-01, 5.018369724442092e-01, 4.752902962082383e-01, 4.486552956056652e-01, 4.220281118338883e-01, 3.955057965950340e-01, 3.691875990296320e-01, 3.431732847389720e-01, 3.175633015043183e-01, 2.924566408966782e-01, 2.679463783886042e-01, 2.441231331518492e-01, 2.210718537110466e-01, 1.988719153219592e-01, 1.775967625327044e-01, 1.573148583944310e-01, 1.380903364946733e-01, 1.199837497591550e-01, 1.030525757797769e-01, +8.735085011789188e-02, 7.292811584897502e-02, 5.982732244758056e-02, 4.808178837444506e-02, 3.771135297837851e-02, 2.871831923385135e-02, 2.108352028641225e-02, 1.476289412849005e-02, 9.683884928956495e-03, 5.642168789286858e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
[0210] Un ejemplo numérico de función de formación en ventanas W160, para el tamaño de trama N=160 se proporciona aquí por 320 entradas para n = 0... 2N-1. Tal y como se explicó más arriba, los últimos valores pueden ser 0.
+4.595886345493055e-04, 7.919323614002698e-04, 1.227927169310031e-03, 1.783653266717233e-03, 2.479549413444207e-03, 3.329799454594261e-03, 4.353535478916468e-03, 5.564965156664018e-03, 6.986108359341676e-03, 8.629882322202329e-03, 1.051343406844975e-02, 1.265082642578719e-02, 1.506090447446532e-02, 1.775591229287213e-02, 2.075475983187825e-02, 2.406813715401559e-02, 2.771207863541604e-02, 3.169933248543932e-02, 3.604609640533871e-02, 4.076128638095439e-02, 4.586038120884381e-02, 5.135136676471998e-02, 5.724780220726930e-02, 6.355854744461048e-02, 7.029450733434550e-02, 7.745987198268531e-02, 8.506635369887924e-02, 9.311641620512773e-02, 1.016162955027316e-01, 1.105690806271684e-01, 1.199789286645804e-01, 1.298417294090302e-01, 1.401623800497866e-01, 1.509371564593891e-01, 1.621632295622287e-01, 1.738354123649302e-01, 1.859520359191026e-01, 1.985008828937603e-01, 2.114778554475382e-01, 2.248732557074316e-01, 2.386763947872762e-01, 2.528729453658238e-01, 2.674547009618951e-01, 2.824031465430401e-01, 2.977050145264297e-01, 3.133419120661713e-01, 3.292976696294886e-01, 3.455490160824131e-01, 3.620795045342974e-01, 3.788648665671841e-01, 3.958851576591690e-01, 4.131143794748322e-01, 4.305308301005456e-01, 4.481076715576617e-01, 4.658227790464821e-01, 4.836466393241829e-01, 5.015564851667653e-01, 5.195228071176610e-01, 5.375197039843709e-01, 5.555183841040963e-01, 5.734957812557457e-01, 5.914186654649489e-01, 6.092622887527459e-01, 6.269981160888640e-01, 6.446002007776794e-01, 6.620384583071039e-01, 6.792906550106088e-01, 6.963256426589250e-01, 7.131194393772130e-01, 7.296469905863920e-01, 7.458864594794676e-01, 7.618094719403713e-01, 7.773958448163656e-01, 7.926208751337592e-01, 8.074666387233143e-01, 8.219101564897180e-01, 8.359343163788637e-01, 8.495180470826319e-01, 8.626485837105826e-01, 8.753083234662220e-01, 8.874884715160425e-01, 8.991737724042251e-01, 9.103527429187326e-01, 9.210144133066616e-01, 9.311556192776946e-01, 9.407644740241826e-01, 9.498382236872068e-01, 9.583732599601223e-01, 9.663690412284377e-01, 9.738235617865406e-01, 9.807442506043361e-01, 9.871297972052695e-01, 9.929872268444632e-01, 9.983241398929388e-01, 1.003150760219063e+00, 1.007473713377193e+00, 1.011309151636166e+00, 1.014666681083198e+00, 1.017563337333301e+00, 1.020014681326785e+00, 1.022039872150903e+00, 1.023654257342442e+00, 1.024881624147540e+00, 1,025739288978437e+00, 1.026250709375593e+00, 1.026436666375082e+00, 1.026320857404224e+00, 1.025922917798664e+00, 1.025269979527211e+00, 1.024382188798244e+00, 1.023284940887058e+00, 1.022000829220643e+00, 1.020555973231408e+00, 1.018971390778550e+00, 1.017275179369116e+00, 1.015489129111694e+00, 1.013639356938881e+00, 1.011747750709711e+00, 1.009840844244693e+00, 1.007939764480188e+00, 1.006407400915498e+00, 1.004374825095777e+00, 1.002469814737132e+00, 1.000689073754539e+00, 9.990346001249977e-01, 9.975024904153303e-01, 9.960941547576162e-01, 9.948051243621099e-01, 9.936362728142866e-01, 9.925826537087717e-01, 9.916447007525191e-01, 9.908170758245324e-01, 9.900998445795673e-01, 9.894873685512386e-01, 9.889794323427195e-01, 9.885701787626714e-01, 9.882591911282058e-01, 9.880404423341358e-01, 9.879133688360181e-01, 9.878718098237022e-01, 9.879150762106034e-01, 9.880368938846610e-01, 9.882364564839506e-01, 9.885073687439192e-01, 9.888487088987707e-01, 9.892539488627546e-01, 9.897220412447528e-01, 9.902463287269285e-01, 9.908256340476208e-01, 9.914531811725067e-01, 9.921276814881759e-01, 9.928422499725458e-01, 9.935955098307742e-01, 9.943804814776256e-01, 9.951957244449919e-01, 9.960341878404958e-01, 9.968943831870675e-01, 9.977692009836100e-01, 9.986571134591464e-01, 9.995509738170480e-01, 1.000449227898040e+00, 1.001344692310058e+00, 1.002235786606954e+00, 1.003115291715261e+00, 1.003981602446902e+00, 1.004827468041713e+00, 1.005651275972376e+00, 1.006445772052972e+00, 1.007209352772459e+00, 1.007934783656087e+00, 1.008620496650569e+00, 1.009259314290145e+00, 1.009849742422788e+00, 1.010384692193296e+00, 1.010862783160582e+00, 1.011277044709547e+00, 1.011626247430694e+00, 1.011903571699736e+00, 1.012107954864219e+00, 1.012232755709885e+00, 1.012277089047072e+00, 1.012234505114778e+00, 1.012104319978655e+00, 1.011880293122688e+00, 1.011561972516341e+00, 1.011143373963981e+00, 1.010624321020038e+00, 1.009999148545101e+00, 1.009268031808824e+00, 1.008425698479647e+00, 1.007472774447058e+00, 1.006404483571931e+00, 1.005222003295591e+00, 1.003921160689206e+00, 1.002503762756151e+00, 1.000966332772540e+00, 9.993114007411373e-01, 9.975362702189898e-01, 9.956442306333592e-01, 9.936333924912825e-01, +9.908677480361242e-01, 9.882326326262749e-01, 9.853620567056602e-01, 9.822305093671991-01, 9.788185853162172e-01, 9.751026333215268e-01, 9.710631852370086e-01, 9.666759668947944e-01, 9.619242192293307e-01, 9.567841986369235e-01, 9.512394303101863e-01, 9.452700238623795e-01, 9.388615698236068e-01, 9.319946435581106e-01, 9.246592033932568e-01, 9.168383396399868e-01, 9.085218034087421e-01, 8.996967011299613e-01, 8.903562054918268e-01, 8.804877931535187e-01, 8.700884209228057e-01, 8.591492134848259e-01, 8.476686394755906e-01, 8.356428970797861e-01, 8.230753889817990e-01, 8.099649296155544e-01, 7.963204506324437e-01, 7.821460539775005e-01, 7.674541821769616e-01, 7.522563457568547e-01, 7.365702052057368e-01, 7.204090552899627e-01, 7.037975107157410e-01, 6.867542812151157e-01, 6.693041888771051e-01, 6.514710959179395e-01, 6.332854832820911e-01, 6.147685389896460e-01, 5.959553778639692e-01, 5.768737955463938e-01, 5.575534287167304e-01, 5.380320138068979e-01, 5.183454027643563e-01, 4.985259415650634e-01, 4.786156067459849e-01, 4.586473038370941e-01, 4.386643656872842e-01, 4.187046888325280e-01, 3.988123056192917e-01, 3.790262923635886e-01, 3.593914828698096e-01, 3.399474132903109e-01, 3.207392420889753e-01, 3.018061113177048e-01, 2.831905952786929e-01, 2.649288369241889e-01, 2.470608550624402e-01, 2.296201119084317e-01, 2.126433716126151e-01, 1.961601816145380e-01, 1.802035203864437e-01, 1.647996883470626e-01, 1.499787548077656e-01, 1.357643522991611e-01, 1.221842534547464e-01, 1.092601994264172e-01, 9.701788451015501e-02, 8.547680283183663e-02, 7.465976378295235e-02, 6.458254322751883e-02, 5.526281189874138e-02, 4.670976978373095e-02, 3.893244425578719e-02, 3.192976013776996e-02, 2.569810636390756e-02, 2.022259265088492e-02, 1.548317776486452e-02, 1.144924909653903e-02, 8.076482660383199e-03, 5.300044080947794e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
[0211] Un ejemplo numérico de función de formación en ventanas W240, para el tamaño de trama N=240 se proporciona aquí (480 muestras):
+4.090106504820579e-04 6.143388180964179e-04 8.571759876954877e-04 1.147015057857495e-03 1.489582832987000e-03 1.889770382231583e-03 2.353000800169909e-03 2.884104959764029e-03 3.488213786635855e-03 4.170040431489613e-03 4.934298832466617e-03 5.787076505403503e-03 6.733811743137561e-03 7.779130464154915e-03 8.927044958757816e-03 1.018202888968871e-02 1.154910606525086e-02 1.303349217699797e-02 1.463951288465963e-02 1.637155619860352e-02 1.823455383898077e-02 2.023309488998589e-02 2.237116158648752e-02 2.465237348403478e-02 2.708101935270475e-02 2.966159685753317e-02 3.239884850877327e-02 3.529601774976465e-02 3.835663329277230e-02 4.158447932459513e-02 4.498322421745353e-02 4.855610986150206e-02 5.230596475016741e-02 5.623624576084146e-02 6.035055738891727e-02 6.465186317477950e-02 6.914195749790462e-02 7.382288203064732e-02 7.869709331995660e-02 8.376761638427657e-02 8.903563687211118e-02 9.450199243028472e-02 1.001680193006426e-01 1.060356225286319e-01 1.121060220821844e-01 1.183788547045326e-01 1.248534855777947e-01 1.315302847610869e-01 1.384103079528939e-01 1.454931890869180e-01 1.527772946853750e-01 1.602608842337125e-01 1.679435556337752e-01 1.758245615079801e-01 1.839020119821303e-01 1.921728622634411e-01 2.006344295681524e-01 2.092853879977170e-01 2.181238261985594e-01 2.271462264407930e-01 2.363479205237173e-01 2.457259744642953e-01 2.552771551741124e-01 2.649981094228982e-01 2.748839432649996e-01 2.849296444030153e-01 2.951306505827265e-01 3.054824712370942e-01 3.159799638238941e-01 3.266169794538543e-01 3.373873799614014e-01 3.482855915638277e-01 3.593057693987583e-01 3.704415932452488e-01 3.816862385160692e-01 3.930329782788047e-01 4.044749630814483e-01 4.160051103939122e-01 4.276159595085598e-01 4.393004362003260e-01 4.510516333434032e-01 4.628616046119925e-01 4.747225454237193e-01 4.866266705542529e-01 4.985664508456704e-01 5.105341492548225e-01 5.225212793188740e-01 5.345190505841265e-01 5.465201916422433e-01 5.585172769552711e-01 5.705021536899105e-01 5.824658100332457e-01 5.943991720381216e-01 6.062948176207270e-01 6.181452662624718e-01 6.299422016714543e-01 6.416768736044914e-01 6.533411462740817e-01 6.649277540000037e-01 6.764292700223311e-01 6.878367295965062e-01 6.991421467689277e-01 7.103379606632721e-01 7.214176027060971e-01 7.323746102405828e-01 7.432008025932804e-01 7.538887973483771e-01 7.644315495717613e-01 7.748223151443820e-01 7.850546571907628e-01 7.951223518167163e-01 8.050193862201107e-01 8.147397447696774e-01 8.242774413707643e-01 8.336267114335371e-01 8.427819363777799e-01 8.517386186427548e-01 8.604920874939698e-01 8.690376742017057e-01 8.773720451249032e-01 8.854927938913381e-01 8.933935477349644e-01 9.010727088526728e-01 9.085249398881980e-01 +9.157483563218768e-01, 9.227413839712016e-01, 9.295017469413066e-01, 9.360270196617569e-01, 9.423143052164881e-01, 9.483629792665091e-01, 9.541731142261065e-01, 9.597438382130120e-01, 9.650738394220176e-01, 9.701635474343885e-01, 9.750143364412617e-01, 9.796277191617885e-01, 9.840036439809510e-01, 9.881426772731259e-01, 9.920470446911211e-01, 9.957199420334376e-01, 9.991640812275709e-01, 1.002381307710643e+00, 1.005374268639838e+00, 1.008146718214831e+00, 1.010703123647275e+00, 1.013046655758663e+00, 1.015181271161417e+00, 1.017111643578857e+00, 1.018843380560658e+00, 1.020381713994816e+00, 1.021731101971518e+00, 1.022896948293643e+00, 1.023885455671576e+00, 1.024702974608899e+00, 1.025355286710874e+00, 1.025848243050604e+00, 1.026188366261215e+00, 1.026382881625701e+00, 1.026438102255574e+00, 1.026360125820994e+00, 1.026155530733488e+00, 1.025831456886557e+00, 1.025395432284244e+00, 1.024853974580724e+00, 1.024213482124578e+00, 1.023481184943025e+00, 1.022664602721801e+00, 1.021770903480975e+00, 1.020806917660529e+00, 1.019779396547454e+00, 1.018695995335235e+00, 1.017564416918053e+00, 1.016391686789653e+00, 1.015184918030332e+00, 1.013950835315021e+00, 1.012697033320358e+00, 1.011430749860716e+00, 1.010158346781076e+00, 1.008885191761748e+00, 1.007592718305943e+00, 1.006805603478092e+00, 1.005378742804807e+00, 1.004049051787112e+00, 1.002778356298787e+00, 1.001563778373068e+00, 1.000404915291105e+00, 9.993014844615166e-01, 9.982531564931281e-01, 9.972595460676951e-01, 9.963202131848272e-01, 9.954346644968789e-01, 9.946023543844607e-01, 9.938226881029791e-01, 9.930950268060122e-01, 9.924186919309267e-01, 9.917929657090736e-01, 9.912170911359961e-01, 9.906902760441473e-01, 9.902117003786811e-01, 9.897805192546193e-01, 9.893958602389157e-01, 9.890568243690241e-01, 9.887624937408933e-01, 9.885119364350415e-01, 9.883042028597552e-01, 9.881383235740961e-01, 9.880133161159576e-01, 9.879281898513085e-01, 9.878819413827574e-01, 9.878735508484809e-01, 9.879019873841568e-01, 9259582959+5696965e-01, 9.880651778500144e-01, 9.881978162133899e-01, 9.883630508181326e-01, 9.885597957603544e-01, 9.887869526128024e-01, 9.890434070785485e-01, 9.893280319166613e-01, 9.896396899060125e-01, 9.899772316163624e-01, 9.903394929409673e-01, 9.907252968668226e-01, 9.911334564321237e-01, 9.915627747807666e-01, 9.920120436855326e-01, 9.924800441092685e-01, 9.929655482846576e-01, 9.934673212537685e-01, 9.939841207305906e-01, 9.945146969322154e-01, 9.950577931942117e-01, 9.956121471675398e-01, 9.961764915534302e-01, 9.967495543671935e-01, 9.973300590248015e-01, 9.979167245036720e-01, 9.985082643417953e-01, 9.991033633647473e-01, 9.997003478609010e-01, 1.000299741957418e+00, 1.000897441314013e+00, 1.001493964257960e+00, 1.002087624593489e+00, 1.002677088643863e+00, 1.003261045483858e+00, 1.003838183774652e+00, 1.004407190937699e+00, 1.004966753528881 e+00, 1.005515557572658e+00, 1.006052289109999e+00, 1.006575635258931 e+00, 1.007084285781611e+00, 1.007576934100958e+00, 1.008052277555815e+00, 1.008509017718116e+00, 1.008945862447015e+00, 1.009361528531177e+00, 1.009754742820913e+00, 1.010124241309341e+00, 1.010468769795370e+00, 1.010787087537248e+00, 1.011077969726137e+00, 1.011340205650538e+00, 1.011572597114216e+00, 1.011773962181442e+00, 1.011943138906979e+00, 1.012078982659783e+00, 1.012180362866919e+00, 1.012246166897464e+00, 1.012275305013586e+00, 1.012266707295288e+00, 1.012219319453278e+00, 1.012132107622966e+00, 1.012004064757857e+00, 1.011834207632025e+00, 1.011621572933544e+00, 1.011365223023975e+00, 1.011064253702468e+00, 1.010717792733157e+00, 1.010324996851905e+00, 1.009885057526159e+00, 1.009397209381147e+00, 1.008860731864438e+00, 1.008274947065247e+00, 1.007639223374887e+00, 1.006952983357691e+00, 1.006215708265639e+00, 1.005426938305289e+00, 1.004586273379809e+00, 1.003693377657581 e+00, 1.002747984657666e+00, 1.001749900308864e+00, 1.000699003803502e+00, 9.995952485989262e-01, 9.984386632116344e-01, 9.972293415774932e-01, 9.959672769174924e-01, 9.946500332901397e-01, 9.932403996813470e-01, 9.912511516117244e-01, 9.895756853352172e-01, 9.877713214760662e-01, 9.858577479051078e-01, 9.838303127859196e-01, 9.816822625580078e-01, 9.794074486605805e-01, 9.769999155793757e-01, 9.744528356359687e-01, 9.717597500340699e-01, 9.689141159310996e-01, 9.659101618500662e-01, 9.627421831412876e-01, 9.594038121639412e-01, 9.558889978382734e-01, 9.521922434090249e-01, 9.483086322505029e-01, 9.442332539187503e-01, 9.399607238929982e-01, 9.354860218216989e-01, 9.308052967663477e-01, 9.259146970284931e-01, 9.208101305030523e-01, 9.154873597416558e-01, 9.099426066529104e-01, 9.041732260327581e-01, 8.981763729936715e-01, 8.919490241013392e-01, 8.854882249661838e-01, 8.787919436722827e-01, 8.718585835568161e-01, 8.646864947605047e-01, 8.572738135700366e-01, 8.496195859658071e-01, 8.417237467711145e-01, 8.335862715770727e-01, 8.252074428838668e-01, 8.165875713256009e-01, 8.077280370477699e-01, 7.986311592191131e-01, 7.892986353718001e-01, 7.797330954210866e-01, 7.699379531983687e-01, 7.599171886893816e-01, 7.496758423734833e-01, 7.392176841476761e-01, 7.285474515411827e-01, 7.176714478163359e-01, 7.065962311464494e-01, 6.953282935906302e-01, 6.838739059112046e-01, 6.722395305539791e-01, 6.604334017809461e-01, 6.484643596235256e-01, 6.363395004626368e-01, 6.240661431421666e-01, 6.116530334821534e-01, 5.991098644638286e-01, 5.864461424698465e-01, 5.736694851703749e-01, 5.607881029948401e-01, 5.478160663871271e-01, 5.347619788897301e-01, 5.216365147692703e-01, 5.084499758302256e-01, 4.952135086430446e-01, 4.819387562519412e-01, 4.686361426419003e-01, 4.553170769563941e-01, 4.419939954454178e-01, 4.286789889246267e-01, 4.153837786572842e-01, 4.021211063103491e-01, 3.889032719013054e-01, 3.757425439137077e-01, 3.62651518377631Oe-01, 3.496431418636322e-01, 3.367290822653354e-01, 3.239228075238623e-01, 3.112360816586549e-01, 2.986807941537710e-01, 2.862694673284843e-01, 2.740128472224539e-01, 2.619228330079575e-01, +2.500098438708934e-01, 2.382847225401669e-01, 2.267578490199104e-01, 2.154390996938547e-01, 2.043379825955254e-01, 1.934636765792024e-01, 1.828250319214460e-01, 1.724305860483634e-01, 1.622886348529314e-01, 1.524071880359812e-01, 1.427939789949266e-01, 1.334565845242183e-01, 1.244023922999665e-01, 1.156385879569742e-01, 1.071721547807196e-01, 9.900985872728905e-02, 9.115821766572002e-02, 8.362344855837105e-02, 7.641140367416376e-02, 6.952749039054598e-02, 6.297656454790079e-02, 5.676284244020858e-02, 5.088975408628229e-02, 4.535983304624439e-02, 4.017457306236873e-02, 3.533430192568957e-02, 3.083806062123772e-02, 2.668355420358626e-02, 2.286680405144430e-02, 1.938236337675363e-02, 1.622312720409645e-02, 1.338005016725895e-02, 1.084218595595746e-02, 8.596753980908744e-03, 6.640506529168652e-03, 5.172703110468352e-03, 0.000000000000000e+00, 0.000000000000000e+00 , 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 , 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 , 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
[0212] Un ejemplo numérico de función de formación en ventanas W320, para el tamaño de trama N=320 se proporciona aquí (640 muestras). Tal y como se explicó más arriba, los últimos valores pueden ser 0.
+7.010318350640769e-04 8.910357994632938e-04 1.107726421735994e-03 1.354305556720234e-03 1.632968062524617e-03 1.944392065549996e-03 2.291251920978034e-03 2.676357471188558e-03 3.102160324883627e-03 3.569302917352426e-03 4.080147004222224e-03 4.637409387087253e-03 5.243697651112320e-03 5.900394401532485e-03 6.609908124535202e-03 7.375089966000295e-03 8.197610411215884e-03 9.078195201482999e-03 1.001888876231112e-02 1.102272421949215e-02 1.209201783148431e-02 1.322773320467288e-02 1.443170227861997e-02 1.570673344965518e-02 1.705481769961258e-02 1.847711280171765e-02 1.997546609433320e-02 2.155255505248360e-02 2.320993080187466e-02 2.494800748775296e-02 2.676898100961685e-02 2.867550388692567e-02 3.066976865911597e-02 3.275241094528637e-02 3.492474656851959e-02 3.718932683936013e-02 3.954748420753697e-02 4.200013716597904e-02 4.454866443036003e-02 4.719547798640356e-02 4.994161943600844e-02 5.278755308483513e-02 5.573471840677637e-02 5.878567633813699e-02 6.194176167634657e-02 6.520301218579141e-02 6.857009288032996e-02 7.204473108503576e-02 7.562815385274406e-02 7.932038618419741e-02 8.312281225703541e-02 8.703660776989294e-02 9.106251913073614e-02 9.519952848393795e-02 9.944854075501454e-02 1.038112769854394e-01 1.082885168352610e-01 1.128793060660070e-01 1.175834766182813e-01 1.224015773361210e-01 1.273338065186211e-01 1.323793987456491e-01 1.375389612590117e-01 1.428131506368226e-01 1.482015069292479e-01 1.537021065265166e-01 1.593143180431248e-01 1.650390046254505e-01 1.708759773387028e-01 1.768238156096776e-01 1.828814674176937e-01 1.890485613515956e-01 1.953239376543276e-01 2.017057139908492e-01 2.081934824879514e-01 2.147873518665726e-01 2.214861559453727e-01 2.282869811837961e-01 2.351877543503455e-01 2.421885165595468e-01 2.492877833071390e-01 2.564833108170047e-01 2.637736050921935e-01 2.711575593740559e-01 2.786328295517739e-01 2.861965981859126e-01 2.938469307293017e-01 3.015829286213736e-01 3.094025219039914e-01 3.173023310827802e-01 3.252796888787393e-01 3.333329987313211e-01 3.414597523183469e-01 3.496568059948401e-01 3.579215403419018e-01 3.662523018706806e-01 3.746461722601965e-01 3.830993933108193e-01 3.916090507233831e-01 4.001732470818926e-01 4.087890872349265e-01 4.174524354370054e-01 4.261601728427663e-01 4.349103424521226e-01 4.436999665749521e-01 4.525250566690236e-01 4.613821390145840e-01 4.702690556535691e-01 4.791821288489955e-01 4.881175853001019e-01 4.970720120437943e-01 5.060433154467696e-01 5.150277508616620e-01 5.240208300352607e-01 5.330187387865785e-01 5.420196856030712e-01 5.510201184135838e-01 5.600165101133929e-01 5.690047761849362e-01 5.779823098049300e-01 5.869449780892492e-01 5.958886225335936e-01 6.048099568741729e-01 6.137068698395559e-01 6.225761217125432e-01 6.314128591964590e-01 6.402134772829997e-01 6.489754897736506e-01 6.576959114103553e-01 6.663704870510495e-01 6.749962795110787e-01 6.835701860237697e-01 6.920890588499607e-01 7.005478826218464e-01 7.089444008783498e-01 7.172765338080037e-01 7.255415386736762e-01 7.337354140683028e-01 7.418546544582220e-01 7.498972580176051e-01 7.578599326607545e-01 7.657390988438872e-01 7.735317637507610e-01 7.812362247368221e-01 7.888499478365373e-01 7.963691608881653e-01 8.037915368847273e-01 8.111154166403033e-01 +8.183384161720055e-01, 8.254567363530231e-01, 8.324682688387346e-01, 8.393715063470556e-01, 8.461645428100565e-01, 8.528442051510350e-01, 8.594088830061699e-01, 8.658575289268042e-01, 8.721883611259660e-01, 8.783992457627015e-01, 8.844895714000796e-01, 8.904559910537616e-01, 8.962997945931150e-01, 9.020168984242400e-01, 9.076056139480890e-01, 9.130664170641334e-01, 9.183979162084582e-01, 9.235994678560167e-01, 9.286692422352107e-01, 9.336076279434850e-01, 9.384129048732400e-01, 9.430836933050435e-01, 9.476197145049868e-01, 9.520221006942875e-01, 9.562904165806793e-01, 9.604235518327253e-01, 9.644205605875820e-01, 9.682827690312492e-01, 9.720106722663890e-01, 9.756042291745447e-01, 9.790638238608151e-01, 9.823902028722666e-01, 9.855837812929384e-01, 9.886436665180195e-01, 9.915714515450228e-01, 9.943692859110803e-01, 9.970385179500313e-01, 9.995787919228785e-01, 1.001991256344717e+00, 1.004277707367492e+00, 1.006439806897506e+00, 1.008478224880801e+00 1.010395057449511e+00, 1.012192316076366e+00, 1.013871638199171e+00, 1.015433826923486e+00 1.016881083871244e+00, 1.018216717878600e+00, 1.019442870837515e+00, 1.020560853084751e+00 1.021572361827679e+00, 1.022480682703848e+00, 1.023288268237906e+00, 1.023997104737320e+00 1.024609726504572e+00, 1.025129444345768e+00, 1.025558707847599e+00, 1.025899187425550e+00 1.026153736073730e+00, 1.026326400217514e+00, 1.026419755159132e+00, 1.026435753513555e+00 1.026376745497183e+00, 1.026246413164014e+00, 1.026047802601159e+00, 1.025783163725466e+00 1.025455636062312e+00, 1.025068712226252e+00, 1.024625269765159e+00, 1.024127035189888e+00 1.023577282345944e+00, 1.022979990313458e+00, 1.022338337695996e+00, 1.021654354624439e+00 1.020930844259280e+00, 1.020171385028845e+00, 1.019379551852598e+00, 1.018557222865231e+00 1.017708008483692e+00, 1.016835630605444e+00, 1.015943000562828e+00, 1.015032211107897e+00 1.014106040189062e+00, 1.013168810057302e+00, 1.012223533569952e+00, 1.011272160610958e+00 1.010317161995333e+00, 1.009363573682324e+00, 1.008418957730006e+00, 1.007443035427814e+00 1.006980582693088e+00, 1.005880191360173e+00, 1.004870660907557e+00, 1.003887307826199e+00 1.002933862630671e+00, 1.002012456628431e+00, 1.001122929266782e+00, 1.000264200804259e+00 9.994361518334981e-01, 9.986396025239043e-01, 9.978744044020248e-01, 9.971394126637049e-01, 9.964344374346332e-01, 9.957602381261346e-01, 9.951165794460692e-01, 9.945022689695088e-01, 9.939170480434331e-01, 9.933616056210112e-01, 9.928356667510468e-01, 9.923379640068731e-01, 9.918682011153984e-01, 9.914270132578689e-01, 9.910140670228395e-01, 9.906280727376265e-01, 9.902686735168059e-01, 9.899364775767996e-01, 9.896311064950427e-01, 9.893512408407925e-01, 9.890965020344753e-01, 9.888674481881904e-01, 9.886636955343167e-01, 9.884838850803949e-01, 9.883276240055705e-01, 9.881954463086439e-01, 9.880869460773882e-01, 9.880007538329854e-01, 9.879364462155417e-01, 9.878945575956836e-01, 9.878746493979034e-01, 9.878753499522159e-01, 9.878962158879177e-01, 9.879377642109470e-01, 9.879995488718708e-01, 9.880801746803725e-01, 9.881791937541983e-01, 9.882970966792446e-01, 9.884334355024147e-01, 9.885867883714737e-01, 9.887566952073135e-01, 9.889436358294569e-01, 9.891471384894399e-01, 9.893657732439902e-01, 9.895990550550585e-01, 9.898474573387898e-01, 9.901104832002432e-01, 9.903866926546286e-01, 9.906755858999687e-01, 9.909776136318341e-01, 9.912922749689899e-01, 9.916181054602099e-01, 9.919545975686356e-01, 9.923021872317422e-01, 9.926603609120486e-01, 9.930276450366935e-01, 9.934035125599263e-01, 9.937883997783191e-01, 9.941817792665538e-01, 9.945821646067609e-01, 9.949890245456261e-01, 9.954027843196593e-01, 9.958229139376651e-01, 9.962479146150113e-01, 9.966772475112751e-01, 9.971113385049125e-01, 9.975496462958124e-01, 9.979906675056988e-01, 9.984338592613343e-01, 9.988796523949821e-01, 9.993275431378141e-01, 9.997753812452573e-01, 1.000224669219663e+00, 1.000672909364706e+00, 1.001121604191588e+00, 1.001568597382930e+00 1.002013378040221e+00, 1.002456372686098e+00, 1.002897030034197e+00, 1.003333829980590e+00 1.003766216551067e+00, 1.004194607298016e+00, 1.004618447680436e+00, 1.005036211788027e+00 1.005447348229275e+00, 1.005852270535212e+00, 1.006250425365265e+00, 1.006640290029854e+00 1.007021310029137e+00, 1.007393907701933e+00, 1.007757528772291e+00, 1.008110655922241e+00 1.008452744553207e+00, 1.008784215564761e+00, 1.009104530964226e+00, 1.009412177137242e+00 1.009706620067364e+00, 1.009988296223056e+00, 1.010256673981368e+00, 1.010510261597171e+00 1.010748529051234e+00, 1.010971938438940e+00, 1.011179974034890e+00, 1.011371154144579e+00 1.011544976893053e+00, 1.011701915457469e+00, 1.011841483052088e+00, 1.011962209203063e+00 1.012063621581602e+00, 1.012146211141323e+00, 1.012209509774826e+00, 1.012252080651208e+00 1.012273461473019e+00, 1.012274179329824e+00, 1.012253779830287e+00, 1.012210860152664e+00 1.012144976732521e+00, 1.012056685871527e+00, 1.011945565763788e+00, 1.011810229432951e+00 1.011650280893217e+00, 1.011466289818154e+00, 1.011257880752579e+00, 1.011023694799342e+00 1.010763375755366e+00, 1.010477533938561e+00, 1.010165826445586e+00, 1.009826955798404e+00 1.009460591235290e+00, 1.009067412134881e+00, 1.008647118373303e+00, 1.008198467170796e+00 1.007721196075366e+00, 1.007216031301935e+00, 1.006682757156533e+00, 1.006120180721864e+00 1.005528123164754e+00, 1.004907385380564e+00, 1.004257813991292e+00, 1.003578321293819e+00 1.002868793771428e+00 1.002130123378852e+00, 1.001362250678481e+00, 1.000564166270619e+00 9.997358689793686e-01, 9.988783302889642e-01 9.979915852192069e-01, 9.970747197397686e-01, 9.961277448216609e-01, 9.951529474418550e-01, 9.941541831614942e-01, 9.930678080460911e-01, 9.914646039976289e-01, 9.902352352689523e-01, 9.889131869680553e-01, 9.875383274623817e-01, 9.861028679251979e-01, 9.846041087188396e-01, 9.830394337851476e-01, 9.814052410296346e-01, 9.796987091039431e-01, 9.779184677896273e-01, +9.760616740194450e-01, 9.741245958128935e-01 9.721043782586516e-01 9.699991325531057e-01 9.678068213341133e-01, 9.655234943873925e-01 9.631470850364502e-01 9.606758082762421e-01 9.581070287387355e-01, 9.554372064329766e-01 9.526641870716750e-01 9.497868942084339e-01 9.468034353946915e-01, 9.437103240778303e-01 9.405054771915659e-01 9.371877218082764e-01 9.337553821450042e-01, 9.302057763482381e-01 9.265373496318979e-01 9.227494594741956e-01 9.188401295674290e-01, 9.148067377557749e-01 9.106476709258303e-01 9.063629680720371e-01 9.019514987490371e-01, 8.974108808873397e-01 8.927398817643528e-01 8.879382683346716e-01 8.830050715882986e-01, 8.779385355821995e-01 8.727379973888942e-01 8.674038889082810e-01 8.619352566808824e-01, 8.563305243162549e-01 8.505893287555129e-01 8.447127297770400e-01 8.387007637143140e-01, 8.325523768291013e-01 8.262677444285360e-01 8.198478927378535e-01 8.132935411236417e-01, 8.066040997239516e-01 7.997809105802602e-01 7.928255537687610e-01 7.857391245481645e-01, 7.785212684545030e-01 7.711744403395434e-01 7.637008160854790e-01 7.561026668755407e-01, 7.483805701761127e-01 7.405363749469933e-01 7.325730245135402e-01 7.244930008228270e-01, 7.162980305440977e-01 7.079910089690906e-01 6.995757887359807e-01 6.910546259244099e-01, 6.824295471401947e-01 6.737031265887281e-01 6.648801659515325e-01 6.559637902883004e-01, 6.469573547411541e-01 6.378629377753962e-01 6.286855280775698e-01 6.194273058858271e-01, 6.100922809170846e-01 6.006842631336996e-01 5.912087588215279e-01 5.816678990293079e-01, 5.720650011081139e-01 5.624031153715043e-01 5.526906296747590e-01 5.429296335729603e-01, 5.331253296256703e-01 5.232805923025862e-01 5.134010079652535e-01 5.034916218473681e-01, 4.935565059779637e-01 4.835996679580253e-01 4.736270399539165e-01 4.636428606356920e-01, 4.536519115376573e-01 4.436589520558524e-01 4.336702110092904e-01 4.236905139305571e-01, 4.137241358370227e-01 4.037764981593496e-01 3.938536636599411e-01 3.839608678121244e-01, 3.741023650337649e-01 3.642834353302138e-01 3.545105744959439e-01 3.447887254766501e-01, 3.351225758795436e-01 3.255174149216463e-01 3.159783340225490e-01 3.065118829951374e-01, 2.971215837581699e-01 2.878124834032541e-01 2.785898831431837e-01 2.694592444601873e-01, 2.604240268886858e-01 2.514886909115454e-01 2.426587307354934e-01 2.339385917103926e-01, 2.253316454409216e-01 2.168420127437019e-01 2.084745870335012e-01 2.002332724591125e-01, 1.921209969418307e-01 1.841414579810840e-01 1.762991374092108e-01 1.685975427109672e-01, 1.610392647455030e-01 1.536276387455411e-01 1.463667950599712e-01 1.392599476606262e-01, 1.323093893293405e-01 1.255182155111708e-01 1.188903216873086e-01 1.124286726877977e-01, 1.061353122093495e-01 1.000130754353283e-01 9.406556557413207e-02 8.829543394466104e-02, 8.270438757849530e-02 7.729486433686703e-02 7.206998099643687e-02 6.703183558090599e-02, 6.218153160076208e-02 5.752079270262547e-02 5.305187265543024e-02 4.877591488398974e-02, 4.469299727922282e-02 4.080367800167831e-02 3.710883802024244e-02 3.360819061792393e-02, 3.030027537135876e-02 2.718416076819826e-02 2.425872983336823e-02 2.152170070657780e-02, 1.896992105664512e-02 1.660053693426304e-02 1.441002712765955e-02 1.239334766429038e-02, 1.054549096241532e-02 8.862485552559351e-03 7.329085750247888e-03 5.896299968476346e-03, 4.914753459788711e-03 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00 0.000000000000000e+00
[0213] Un ejemplo numérico de función de formación en ventanas W480, para el tamaño de trama N=480 se proporciona aquí (960 muestras). Tal y como se explicó más arriba, los últimos valores pueden ser 0.
+5.595519647227489e-04, 6.718404887323839e-04, 7.919323614002698e-04, 9.254835101516548e-04, 1.069418485858920e-03, 1.227927169310031e-03, 1.398277791978983e-03, 1.584491535026729e-03, 1.783653266717233e-03, 1.999873692180148e-03, 2.230687004705732e-03, 2.479549413444207e-03, +2.744274680521470e-03 3.028517203082985e-03 3.329799454594260e-03 3.651493788541270e-03 3.991659081158673e-03 4.353535478916468e-03 4.734803493964832e-03 5.139354888882466e-03 5.564965156664017e-03 6.015065135312130e-03 6.487669532207667e-03 6.986108359341676e-03 7.507986430774601e-03 8.056692238103912e-03 8.629882322202329e-03 9.230898632007642e-03 9.857619542786990e-03 1.051343406844975e-02 1.119617236058772e-02 1.190938692951881e-02 1.265082642578719e-02 1.342375201935177e-02 1.422598597626579e-02 1.506090447446532e-02 1.592611511144210e-02 1.682519266177794e-02 1.775591229287213e-02 1.872166356881472e-02 1.972014746423546e-02 2.075475983187825e-02 2.182299926812682e-02 2.292828566629717e-02 2.406813715401559e-02 2.524583465017564e-02 2.645943128544517e-02 2.771207863541604e-02 2.900157039370381e-02 3.033143686044867e-02 3.169933248543932e-02 3.310834554878132e-02 3.455615910816914e-02 3.604609640533871e-02 3.757564512209753e-02 3.914808612511974e-02 4.076128638095439e-02 4.241834056741758e-02 4.411695502674887e-02 4.586038120884381e-02 4.764607953574337e-02 4.947719681327219e-02 5.135136676471998e-02 5.327183246133368e-02 5.523619574402436e-02 5.724780220726930e-02 5.930419525733627e-02 6.140861916695377e-02 6.355854744461048e-02 6.575698564821578e-02 6.800132774040281e-02 7.029450733434550e-02 7.263424529955659e-02 7.502357150869594e-02 7.745987198268531e-02 7.994662730757418e-02 8.248121208201259e-02 8.506635369887924e-02 8.769965758141890e-02 9.038399472465716e-02 9.311641620512773e-02 9.590005739506280e-02 9.873233942897164e-02 1.016162955027316e-01 1.045493607096311e-01 1.075345731608719e-01 1.105690806271684e-01 1.136556251529813e-01 1.167913767515824e-01 1.199789286645804e-01 1.232155302990620e-01 1.265040684552515e-01 1.298417294090302e-01 1.332315661550852e-01 1.366709127560524e-01 1.401623800497866e-01 1.437031543339276e-01 1.472957921567060e-01 1.509371564593891e-01 1.546298983040232e-01 1.583709932021852e-01 1.621632295622287e-01 1.660038996795837e-01 1.698955982096184e-01 1.738354123649302e-01 1.778260015982545e-01 1.818640789446629e-01 1.859520359191026e-01 1.900868218108653e-01 1.942708017706291e-01 1.985008828937603e-01 2.027798260494142e-01 2.071046414574582e-01 2.114778554475382e-01 2.158964254821512e-01 2.203627179356420e-01 2.248732557074316e-01 2.294303802774835e-01 2.340304946493155e-01 2.386763947872762e-01 2.433647632018021e-01 2.480980084587409e-01 2.528729453658238e-01 2.576919809402799e-01 2.625518239753811e-01 2.674547009618951e-01 2.723969864831702e-01 2.773809014717047e-01 2.824031465430401e-01 2.874658392896952e-01 2.925657097525320e-01 2.977050145264297e-01 3.028802866809923e-01 3.080937708388026e-01 3.133419120661713e-01 3.186267330325243e-01 3.239446274586855e-01 3.292976696294886e-01 3.346822587497995e-01 3.401004975161905e-01 3.455490160824131e-01 3.510297825670005e-01 3.565392648316303e-01 3.620795045342974e-01 3.676468198385683e-01 3.732431609065464e-01 3.788648665671841e-01 3.845139947587731e-01 3.901867575702975e-01 3.958851576591690e-01 4.016055596175310e-01 4.073498814407726e-01 4.131143794748322e-01 4.189008731078437e-01 4.247056871121635e-01 4.305308301005456e-01 4.363724468005679e-01 4.422326205247767e-01 4.481076715576617e-01 4.539992478845187e-01 4.599036262256764e-01 4.658227790464821e-01 4.717526717360889e-01 4.776951277513855e-01 4.836466393241829e-01 4.896089037533445e-01 4.955781691142885e-01 5.015564851667653e-01 5.075397341675292e-01 5.135297950483941e-01 5.195228071176610e-01 5.255203889406241e-01 5.315186369941947e-01 5.375197039843709e-01 5.435197203416460e-01 5.495204053284317e-01 5.555183841040963e-01 5.615153912741460e-01 5.675072245552497e-01 5.734957812557457e-01 5.794770758870604e-01 5.854526176188222e-01 5.914186654649489e-01 5.973773282523112e-01 6.033245382283379e-01 6.092622887527459e-01 6.151869491458284e-01 6.211002315674210e-01 6.269981160888640e-01 6.328823912226461e-01 6.387491304847892e-01 6.446002007776794e-01 6.504316924413531e-01 6.562457600042717e-01 6.620384583071039e-01 6.678117513456276e-01 6.735619658538692e-01 6.792906550106088e-01 6.849937204005565e-01 6.906734235708962e-01 6.963256426589250e-01 7.019517880051427e-01 7.075491663942173e-01 7.131194393772130e-01 7.186585770351414e-01 7.241690155466505e-01 7.296469905863920e-01 7.350940240070911e-01 7.405065029424016e-01 7.458864594794676e-01 7.512298245353598e-01 7.565387020584289e-01 7.618094719403713e-01 7.670441227603888e-01 7.722388831102434e-01 7.773958448163656e-01 7.825113901786742e-01 7.875876391562497e-01 7.926208751337592e-01 7.976131629355570e-01 8.025610715609228e-01 8.074666387233143e-01 8.123261531893655e-01 8.171419338595847e-01 8.219101564897180e-01 8.266329452432137e-01 8.313069432125857e-01 8.359343163788637e-01 8.405111871797961e-01 8.450403211238631e-01 8.495180470826319e-01 8.539464819668052e-01 8.583225792686004e-01 8.626485837105826e-01 8.669206756254478e-01 8.711415846800790e-01 8.753083234662220e-01 8.794234355078734e-01 8.834826778788665e-01 8.874884715160425e-01 8.914384774585629e-01 8.953346996622868e-01 8.991737724042251e-01 9.029574074899029e-01 9.066828541224163e-01 9.103527429187326e-01 9.139638342168577e-01 9.175184878836662e-01 9.210144133066616e-01 9.244537632557187e-01 9.278332160151861e-01 9.311556192776946e-01 9.344176283021008e-01 9.376215186479845e-01 9.407644740241826e-01 9.438492190005341e-01 9.468728540294310e-01 9.498382236872068e-01 9.527426712456687e-01 9.555885737210712e-01 9.583732599601223e-01 9.610993609218629e-01 9.637636503225360e-01 9.663690412284377e-01 9.689132689491541e-01 9.713988678700001e-01 9.738235617865406e-01 9.761902903500818e-01 9.784963361871022e-01 9.807442506043361e-01 9.829315352320943e-01 9.850609512273165e-01 +9.871297972052695e-01, 9.891408802831312e-01, 9910923625580078e-01, 9.929872268444632e-01, 9.948228821209419e-01, 9.966027455323081e-01, 9983241398929388e-01, 9.999898494568836e-01, 1.001597808884145e+00 1.003150760219063e+00, 1.004646500318265e+00, 1.006088248744700e+00, 1.007473713377193e+00 1.008806248810530e+00,+ 1.010083776257753e+00, 1.011309151636166e+00, 1.012480196393275e+00 1.013600067830152e+00, 1.014666681083198e+00, 1.015683082766535e+00, 1.016647533889674e+00 1.017563337333301e+00, 1.018428468753963e+00, 1.019246216134229e+00, 1.020014681326785e+00 1.020736921761459e+00, 1.021410866072808e+00, 1.022039872150903e+00, 1.022622059577585e+00 1.023160749941404e+00, 1.023654257342442e+00, 1.024105973101631e+00, 1.024514004504684e+00 1.024881624147540e+00, 1.025207065371760e+00, 1.025493542877243e+00, 1.025739288978437e+00 1.025947636692103e+00, 1.026116939910040e+00, 1.026250709375593e+00, 1.026347260729698e+00 1.026409787584788e+00, 1.026436666375082e+00, 1.026431212267978e+00, 1.026391488022762e+00 1.026320857404224e+00, 1.026217843764236e+00, 1.026085730009027e+00, 1.025922917798664e+00 1.025733019213987e+00, 1.025514292433933e+00, 1.025269979527211e+00, 1.024998528084259e+00 1.024703212795365e+00 1.024382188798244e+00, 1 .024039051426278e+00,
+1.023672163232710e+00 1.023284940887058e+00, 1.022875917162315e+00, 1.022448453314994e+00, 1.022000829220643e+00 1.021536599728231e+00, 1.021053875701803e+00, 1.020555973231408e+00, 1.020041434676317e+00 1.019513866799503e+00, 1.018971390778550e+00, 1.018417599116053e+00, 1.017851066303933e+00 1.017275179369116e+00, 1.016688023745155e+00, 1.016093242802983e+00, 1.015489129111694e+00 1.014878956980025e+00, 1.014261064091392e+00, 1.013639356938881e+00, 1.013011559583153e+00 1.012381741769641e+00, 1.011747750709711e+00, 1.011113332101179e+00, 1.010476167900044e+00 1.009840844244693e+00, 1.009204021773819e+00, 1.008572045006596e+00, 1.007939764480188e+00 1.007331850775798e+00, 1.007112182697132e+00, 1.006407400915498e+00, 1.005715372118122e+00 1.005038785533845e+00, 1.004374825095777e+00, 1.003726291405694e+00, 1.003090358040736e+00 1.002469814737132e+00, 1.001861838147367e+00, 1.001269198108365e+00, 1.000689073754539e+00 1.000124220942757e+00, 9.995718119556711e-01, 9.990346001249977e-01, 9.985097406611592e-01 9.979999918405413e-01, 9.975024904153303e-01, 9.970199948970832e-01, 9.965496346682551e-01 9.960941547576162e-01 , 9.956506910018569e-01, 9.952219662800089e-01 9.948051243621099e-01 9.944028741276870e-01 , 9.940123528373235e-01, 9.936362728142866e-01 9.932717517525477e-01 9.929215102130406e-01 , 9.925826537087717e-01, 9.922578948824415e-01 9.919443474477135e-01 9.916447007525191e-01 , 9.913560821234982e-01, 9.910811659133294e-01 9.908170758245324e-01 9.905664908867821e-01 , 9.903265196045258e-01, 9.900998445795673e-01 9.898835741176714e-01 9.896803735870122e-01 , 9.894873685512386e-01, 9.893072032520545e-01 9.891370094863634e-01 9.889794323427195e-01 , 9.888315884970242e-01, 9.886961351016699e-01 9.885701787626714e-01 9.884563716748773e-01 , 9.883518302777313e-01, 9.882591911282058e-01 9.881755763473004e-01 9.881036242002076e-01 , 9.880404423341358e-01, 9.879886826752381e-01 9.879454420034824e-01 9.879133688360181e-01 , 9.878895706371619e-01, 9.878766784594818e-01 9.878718098237022e-01 9.878775927630988e-01 , 9.878911354436840e-01, 9.879150762106034e-01 9.879465136687265e-01 9.879880844262307e-01 , 9.880368938846610e-01, 9.880955662657537e-01 9.881612121412342e-01 9.882364564839506e-01 , 9.883183975703879e-01, 9.884096731867189e-01 9.885073687439192e-01 9.886141241716089e-01 , 9.887270275540468e-01, 9.888487088987707e-01 9.889762614809646e-01 9.891123127261381e-01 , 9.892539488627546e-01, 9.894038044982261e-01 9.895589571176194e-01 9.897220412447528e-01 , 9.898901380212467e-01, 9.900658706993652e-01 9.902463287269285e-01 9.904341281652976e-01 , 9.906263564100900e-01, 9.908256340476208e-01 9.910290387632859e-01 9.912391966549245e-01 , 9.914531811725067e-01, 9.916736156286597e-01 9.918975763831412e-01 9.921276814881759e-01 , 9.923610074433741e-01, 9.926001740490448e-01 9.928422499725458e-01 9.930898628710855e-01 , 9.933400717991352e-01, 9.935955098307742e-01 9.938532319665272e-01 9.941158706465729e-01 , 9.943804814776256e-01, 9.946496946937963e-01 9.949205650500305e-01 9.951957244449919e-01 , 9.954722223202400e-01, 9.957526959635303e-01 9.960341878404958e-01 9.963193400387707e-01 , 9.966051908036528e-01, 9.968943831870675e-01 9.971839552785087e-01 9.974765480003592e-01 , 9.977692009836100e-01, 9.980645531056329e-01 9.983596442023971e-01 9.986571134591464e-01 , 9.989539982645417e-01, 9.992529406343204e-01 9.995509738170480e-01 9.998507434423984e-01 , 1.000149278838447e+00, 1.000449227898040e+00 1.000747617880619e+00, 1.001047097000738e+00, 1.001344692310058e+00, 1.001643050985813e+00, 1.001939200113204e+00, 1.002235786606954e+00, 1.002529835919150e+00, 1.002823997223967e+00, 1.003115291715261e+00, 1.003406373183356e+00, 1.003694257266035e+00, 1.003981602446902e+00, 1.004265420574493e+00, 1.004548371695603e+00, 1.004827468041713e+00, 1.005105367331224e+00, 1.005379085053508e+00, 1.005651275972376e+00, 1.005918957263603e+00, 1.006184784468940e+00, 1.006445772052972e+00, 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1.012157343029718e+00 1.012104319978655e+00 1.012039603446877e+00, 1.011965913685509e+00, 1.011880293122688e+00 1.011785448628142e+00 1.011678439894684e+00, 1.011561972516341e+00, 1.011433103151726e+00 1.011294553726738e+00 1.011143373963981e+00, 1.010982291036989e+00, 1.010808368434796e+00 1.010624321020038e+00 1.010427231547075e+00, 1.010219813871895e+00, 1.009999148545101e+00 1.009767970668237e+00 1.009523347700539e+00, 1.009268031808824e+00, 1.008999095526602e+00 1.008719286674458e+00 1.008425698479647e+00, 1.008121073095495e+00, 1.007802512993334e+00 1.007472774447058e+00 1.007128952000889e+00, 1.006773824218378e+00, 1.006404483571931e+00 1.006023715042962e+00
+1.005628630023041e+00 1.005222003295591e+00, 1.004800972930542e+00, 1.004368308119956e+00, 1.003921160689206e+00 1.003462311571559e+00 1.002988912076156e+00, 1.002503762756151e+00, 1.002004016208227e+00 1.001492483526354e+00 1.000966332772540e+00, 1.000428371467870e+00, 9.998757944861690e-01 9.993114007411373e-01 9.987324107135600e-01 9.981416218519609e-01 9.975362702189898e-01 9.969191628491259e-01 9.962875422935514e-01 9.956442306333592e-01 9.949864765356604e-01 9.943171077259315e-01 9.936333924912825e-01 9.929380432296178e-01 9.917160727742302e-01 9.908677480361242e-01 9.900143412821714e-01 9.891360093161795e-01 9.882326326262749e-01 9.873035624860487e-01 9.863463238550498e-01 9.853620567056602e-01 9.843478797730104e-01 9.833051513036913e-01 9.822305093671991e-01 9.811260856582836e-01 9.799880424709783e-01 9.788185853162172e-01 9.776142582502931e-01 9.763768210132104e-01 9.751026333215269e-01 9.737939228124395e-01 9.724467635816038e-01 9.710631852370086e-01 9.696397017403771e-01 9.681786285613160e-01 9.666759668947944e-01 9.651341172191925e-01 9.635494800783196e-01 9.619242192293307e-01 9.602543350544703e-01 9.585422731136767e-01 9.567841986369237e-01 9.549824213719248e-01 9.531333627775944e-01 9.512394303101863e-01 9.492969005669868e-01 9.473083933922714e-01 9.452700238623795e-01 9.431841637391052e-01 9.410472222265884e-01 9.388615698236068e-01 9.366234817959531e-01 9.343357002925867e-01 9.319946435581106e-01 9.296028267859759e-01 9.271568160852692e-01 9.246592033932568e-01 9.221062052092852e-01 9.195004240356797e-01 9.168383396399868e-01 9.141224927600506e-01 9.113493760046765e-01 9.085218034087421e-01 9.056363890361683e-01 9.026958474136628e-01 8.996967011299613e-01 8.966416378522284e-01 8.935272411148886e-01 8.903562054918268e-01 8.871250499337346e-01 8.838366845222299e-01 8.804877931535187e-01 8.770812736055238e-01 8.736138336697008e-01 8.700884209228057e-01 8.665016401172241e-01 8.628563075036018e-01 8.591492134848260e-01 8.553833146397594e-01 8.515554376987873e-01 8.476686394755906e-01 8.437199738159921e-01 8.397124082723917e-01 8.356428970797861e-01 8.315145717373513e-01 8.273244136947282e-01 8.230753889817990e-01 8.187646556254478e-01 8.143955052591809e-01 8.099649296155544e-01 8.054763240960976e-01 8.009271179588155e-01 7.963204506324437e-01 7.916533519679438e-01 7.869294361891859e-01 7.821460539775005e-01 7.773057646170487e-01 7.724075191626083e-01 7.674541821769616e-01 7.624428319731227e-01 7.573778165664506e-01 7.522563457568547e-01 7.470817821499429e-01 7.418518832940608e-01 7.365702052057368e-01 7.312341927030358e-01 7.258478768003871e-01 7.204090552899627e-01 7.149213766200488e-01 7.093829112276890e-01 7.037975107157410e-01 6.981626982337203e-01 6.924822574950567e-01 6.867542812151157e-01 6.809822459535158e-01 6.751641683711578e-01 6.693041888771051e-01 6.634003182158815e-01 6.574563319397519e-01 6.514710959179395e-01 6.454477530601381e-01 6.393842401194645e-01 6.332854832820911e-01 6.271477285210396e-01 6.209759156556838e-01 6.147685389896460e-01 6.085293803703800e-01 6.022569117623975e-01 5.959553778639692e-01 5.896228984554688e-01 5.832624455793536e-01 5.768737955463938e-01 5.704590282594502e-01 5.640165022515612e-01 5.575534287167304e-01 5.510670389249083e-01 5.445598110309068e-01 5.380320138069060e-01 5.314874283056712e-01 5.249238143777145e-01 5.183454027643609e-01 5.117512861349316e-01 5.051454054672581e-01 4.985259415650634e-01 4.918987341485414e-01 4.852602812611293e-01 4.786156067459849e-01 4.719635569001799e-01 4.653076657434153e-01 4.586473038370960e-01 4.519865712901121e-01 4.453241417472980e-01 4.386643656872857e-01 4.320060235689271e-01 4.253531733174983e-01 4.187046888325280e-01 4.120648989967404e-01 4.054326930449553e-01 3.988123056192917e-01 3.922024876218684e-01 3.856076044898875e-01 3.790262923635895e-01 3.724631634624147e-01 3.659167460890094e-01 3.593914828698104e-01 3.528864871672291e-01 3.464055764938486e-01 3.399474132903109e-01 3.335176660030293e-01 3.271139090168518e-01 3.207392420889753e-01 3.143954622458083e-01 3.080847161569418e-01 3.018061113177053e-01 2.955645092490569e-01 2.893580088818822e-01 2.831905952786933e-01 2.770614560088827e-01 2.709746519672053e-01 2.649288369241889e-01 2.589278854215034e-01 2.529705733428521e-01 2.470608550624402e-01 2.411974884962474e-01 2.353843453791010e-01 2.296201119084320e-01 2.239085920293915e-01 2.182484277107470e-01 2.126433716126154e-01 2.070920316105701e-01 2.015981078416022e-01 1.961601816145380e-01 1.907818965593135e-01 1.854618027014993e-01 1.802035203864437e-01 1.750055292053725e-01 1.698714235427536e-01 1.647996883470628e-01 1.597938610874129e-01 1.548523838673932e-01 1.499787548077658e-01 + 1.451714001185458e-01, 1.404337947365906e-01, 1.357643522991611e-01, 1.311665152711531e-01, 1.266386794659985e-01, 1.221842534547464e-01, 1.178016171445482e-01, 1.134941442588690e-01, 1.092601994264173e-01, 1.051031184506442e-01, 1.010212496137049e-01, 9.701788451015510e-02, 9.309135143613317e-02, 8.924488982596421e-02, 8.547680283183663e-02, 8.179026694646475e-02, 7.818355556343952e-02, 7.465976378295235e-02, 7.121713409722980e-02, 6.785866241065035e-02, 6.458254322751886e-02, 6.139166651287085e-02, 5.828416955031769e-02, 5.526281189874142e-02, 5.232565602156542e-02, 4.947530987083008e-02, 4.670976978373095e-02, 4.403144898585497e-02, 4.143827607712719e-02, 3.893244425578721e-02, 3.651180398163022e-02, 3.417832280408597e-02, 3.192976013776998e-02, 2.976774716313782e-02, 2.769013516567754e-02, 2.569810636390758e-02, 2.378944369289586e-02, 2.196497565730828e-02, 2.022259265088492e-02, 1.856252261671509e-02, 1.698293043956028e-02, 1.548317776486453e-02, 1.406194554493180e-02, 1.271739094059619e-02, 1.144924909653903e-02, 1.025352572459910e-02, 9.132141467690603e-03, 8.076482660383204e-03, 7.093814769976364e-03, 6.160346335510290e-03, 5.300044080947794e-03, 4.327696566833525e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
[0214] Un ejemplo numérico de función de formación en ventanas, para el tamaño de trama N=960 se propor ciona aquí (1920 muestras). Tal y como se explicó más arriba, los últimos valores pueden ser 0.
+4.346763076430269e-04, 4.841399974556557e-04, 5.337292962876158e-04, 5.864735900759105e-04, 6.428827504324996e-04, 7.010318350640768e-04, 7.608344672311270e-04, 8.240821499679188e-04, 8.910357994632938e-04, 9.604008359868557e-04, 1.032187650884365e-03, 1.107726421735994e-03, 1.187132578842487e-03, 1.269300730654068e-03, 1.354305556720234e-03, 1.443403284874795e-03, 1.536663296357133e-03, 1.632968062524617e-03, 1.732380147404573e-03, 1.836145247521724e-03, 1.944392065549996e-03, 2.056125836181849e-03, 2.171386021601719e-03, 2.291251920978034e-03, 2.415808383814314e-03, 2.544144440874477e-03, 2.676357471188558e-03, 2.813551797283812e-03, 2.955803613263345e-03, 3.102160324883627e-03, 3.252661103181324e-03, 3.408341073385241e-03, 3.569302917352426e-03, 3.734713566068289e-03, 3.904659832213214e-03, 4.080147004222224e-03, 4.261212283030981e-03, 4.446929867132814e-03, 4.637409387087253e-03, 4.833793064672789e-03, 5.036194779738963e-03, 5.243697651112321e-03, 5.456361749675164e-03, 5.675227929566806e-03, 5.900394401532485e-03, 6.131014766883671e-03, 6.367178191275927e-03, 6.609908124535202e-03, 6.859253963058476e-03, 7.114293307371561e-03, 7.375089966000295e-03, 7.642693523739984e-03, 7.917171839712018e-03, 8.197610411215884e-03, 8.484065880416487e-03, 8.777567475206218e-03, 9.078195201482999e-03, 9.385078909241503e-03, 9.698299554301988e-03, 1.001888876231112e-02, 1.034691797503113e-02, 1.068149963936024e-02, 1.102272421949215e-02, 1.137165918496004e-02, 1.172838973544289e-02, 1.209201783148431e-02, 1.246260014549782e-02, 1.284114967210881e-02, 1.322773320467288e-02, 1.362147156562462e-02, 1.402244719763268e-02, 1.443170227861997e-02, + 1.484928966105225e-02 1.527427503031274e-02 1.570673344965518e-02 1.614774906895406e-02 1.659741217225623e-02 1.705481769961258e-02 1.752003567982498e-02 1.799411192217523e-02 1.847711280171765e-02 1.896812570518296e-02 1.946722405557199e-02 1.997546609433320e-02 2.049290306467406e-02 2.101858037652682e-02 2.155255505248360e-02 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8. Bibliografía
[0215]
[1] 3GPP, "Codee for Enhanced Voice Services (EVS); Detailed algorithmic description," [en línea]. Disponible en: http://www.3gpp.org/ftp/Specs/archive/26_series/26.445/26445-d00.zip.
[2] P. P. Julien Faure, "Delay-optimized overlap transform, coding/decoding weighting Windows". Patente de EE. UU. US8847795, 28062011.
[3] Geiger, Audio Coding based on integer transform, Ilmenau: https://www.db-thueringen.de/receive/dbt_mods_00010054, 2004.

Claims (42)

  1. REIVINDICACIONES 1. Un aparato (130, 130A, 110) para codificar una señal de audio que comprende una pluralidad de tramas, en el cual el aparato comprende: una herramienta de transformada con solapamiento modulada (131) para transformar una representación en el dominio de tiempo, TD, de la señal de audio, o una versión procesada de la misma, en una representación en el dominio de la frecuencia, FD, donde la herramienta de transformada con solapamiento modulada (131) está con figurada para efectuar un análisis de transformada con solapamiento modulada mediante una función de formación en ventanas de análisis (40, 50, 70, 240) que presenta una parte de intersección (44, 64, 244) que intersecta con una función lineal (40', 240') en correspondencia con al menos cuatro puntos (#1, #2, #3, #4); y un escritor de flujo de bits (137) configurado para preparar un flujo de bits en base a la representación de FD de la señal de audio o una versión procesada de la misma, en el que la función de formación en ventanas de análisis se define de modo que sea asimétrica, en el que la función de formación en ventanas de análisis (40, 240) se define de modo que sea, en la parte de intersección (44, 94, 244): mayor que la función lineal (40', 240') en un primer intervalo (41, 241) entre un primer punto de intersección (#1) y un segundo punto de intersección (#2); menor que la función lineal (40', 240') en un segundo intervalo (42, 242) entre el segundo punto de intersección (#2) y un tercer punto de intersección (#3); mayor que la función lineal (40', 240') en un tercer intervalo (43, 243) entre el tercer punto de intersección (#3) y un cuarto punto de intersección (#4), en el que la función de formación en ventanas de análisis se define de modo que el valor máximo absoluto (41', 241') esté en uno del primer y del tercer intervalo, caracterizado porque la función lineal (40, 240) es una función constante con valor constante 1.
  2. 2. El aparato según la reivindicación 1, en el que la función de formación en ventanas de análisis (40, 240) se define de modo que el máximo de la función de formación en ventanas de análisis (40, 240) sea menos del 25 % mayor que el valor de la función lineal (40, 240) en el mismo momento.
  3. 3. El aparato según la reivindicación 1, en el que la herramienta de transformada con solapamiento modulada está configurada para: llevar a escala los búferes de entrada temporales y/o los valores de coseno o seno con valores de la función de formación en ventanas de análisis (40, 50, 70, 240).
  4. 4. El aparato según la reivindicación 3, en el que la herramienta de transformada con solapamiento modulada está configurada para utilizar búferes de entrada en forma de t(n )=x(Z — Nf+ n)para n = 0..2NF — 1 — Z, y t(2N — Z n) = 0 para n = 0..Z — 1 dondex(n)es una muestra en el TD de la señal de audio o una versión procesada de la señal de audio en el momento n,Nfes el número de muestras procesadas en una trama, y Z es el número de ceros iniciales en la ventana de transformada con solapamiento modulada.
  5. 5. El aparato según cualquiera de las reivindicaciones anteriores, en el que la herramienta de transformada con solapamiento modulada (131) está configurada para efectuar:
    donde X(k) es el valor de frecuencia de transformada con solapamiento modulada a un índice de frecuenciak, nes el momento, ww(n) es la función de formación en ventanas de análisis,t(n)es un búfer de entrada temporal, yNfes el número de muestras procesadas en una trama.
  6. 6. Un aparato (140, 140A, 120) para decodificar una señal de audio, o una versión procesada de la misma, definida en el dominio de la frecuencia, FD, en el que el aparato comprende: un lector de flujo de bits (141) configurado para leer un flujo de bits que codifica la señal de audio; y una herramienta de transformada con solapamiento inversa modulada (147) configurada para efectuar una síntesis de transformada con solapamiento modulada inversa sobre la señal de audio, o una versión procesada de la misma, mediante una función de formación en ventanas de síntesis (90) que presenta una parte de intersección (94) que intersecta con una función lineal en correspondencia con al menos cuatro puntos (#1, #2, #3, #4), en el que la función de formación en ventanas de síntesis (90, 290) se define para que sea asimétrica, en el que la función de formación en ventanas de síntesis (90, 290) se define de modo que sea, en la parte de intersección (44, 94, 244): mayor que la función lineal en un primer intervalo entre un primer punto de intersección y un segundo punto de intersección; menor que la función lineal en un segundo intervalo entre el segundo punto de intersección y un tercer punto de intersección; mayor que la función lineal en un tercer intervalo entre el tercer punto de intersección y un cuarto punto de intersección, en el que la función de formación en ventanas de síntesis se define de modo que el valor máximo absoluto esté en uno del primer y del tercer intervalo, caracterizado porque la función lineal es una función constante con valor constante 1.
  7. 7. El aparato según la reivindicación 6, en el que la función de formación en ventanas de síntesis (90, 290) se define de modo que el máximo de la función de formación en ventanas de síntesis (90, 290) sea menos del 25 % mayor que el valor de la función lineal (90, 290) en el mismo momento.
  8. 8. El aparato según la reivindicación 6 o 7, en el que la herramienta de transformada con solapamiento modulada inversa (147) está configurada para: llevar a escala los valores en un búfer de alias en el dominio de tiempo con valores de la función de formación en ventanas de síntesis (90).
  9. 9. El aparato según cualquiera de las reivindicaciones 6 a 8, en el que la herramienta de transformada con solapamiento modulada inversa (147) está configurada para generar una representación de señal en el dominio del tiempo, TD, en forma de
    dondet(n)esun búfer de alias,l(fc)es la señal de audio o una versión procesada de la misma, yNfes el número de muestras para una trama en el TD.
  10. 10. El aparato según cualquiera de las reivindicaciones 6 a 9, en el que la herramienta de transformada con solapamiento modulada inversa (147) está configurada para: efectuar una formación en ventanas (S162) del búfer de alias en el tiempo.
  11. 11. El aparato según cualquiera de las reivindicaciones 6 a 10, en el que la herramienta de transformada con solapamiento modulada inversa (147) está configurada para efectuar una operación de formación en ventanas efectuando:
  12. 12. El aparato según cualquiera de las reivindicaciones 6 a 11, en el que la herramienta de transformada con solapamiento modulada inversa (147) está configurada para efectuar una operación de adición con solapamiento (S163).
  13. 13. El aparato según cualquiera de las reivindicaciones 6 a 12, en el que la herramienta de transformada con solapamiento modulada inversa (147) está configurada para efectuar una operación de adición con solapamiento como:
    donde £(n) es el valor de salida,t(.)es un búfer de alias de tiempo dividido en ventanas, yNf esel número de muestras en una trama.
  14. 14. El aparato según cualquiera de las reivindicaciones 6 a 13, en el que: la función de formación en ventanas de síntesis (90) se define de modo que, en la parte de intersección (44, 244), un valor máximo relativo (43', 243') esté en el primer o el tercer intervalo (41,43, 241, 243) y que un valor mínimo relativo (42', 242') esté en el segundo intervalo (42, 242).
  15. 15. El aparato según cualquiera de las reivindicaciones 6 a 14, en el que: la función de formación en ventanas de síntesis (90) se define para presentar, en la parte de intersección (44, 244, 94), un valor mayor que la función lineal en un intervalo que consta del 30 % y del 50 % de dos tramas.
  16. 16. El aparato según la reivindicación 14 o 15, en el que: la función de formación en ventanas de síntesis (90) se define de modo que el máximo de la función de formación en ventanas de síntesis (90) sea menos del 25 % mayor que el valor de la función lineal en el mismo momento.
  17. 17. El aparato según cualquiera de las reivindicaciones 14 a 16, en el que: la función de formación en ventanas de síntesis (90) se define de modo que el máximo (41', 241') de la función de formación en ventanas de síntesis (90) sea menos del 5 % mayor que el valor de la función lineal en el mismo mo mento.
  18. 18. El aparato según cualquiera de las reivindicaciones 14 a 17, en el que: la función de formación en ventanas de síntesis (90) se define de modo que presente una segunda diferenciación numérica entre -3*10-4 y 3*10-4.
  19. 19. El aparato según cualquiera de las reivindicaciones 6 a 18, en el que: la función de formación en ventanas de síntesis (90) se define de modo que presente una tercera diferenciación nu mérica entre -2*10-5 y 2*10-5.
  20. 20. El aparato según cualquiera de las reivindicaciones 6 a 19, que comprende además: un espacio de almacenamiento (113) para almacenar los valores de la función de formación en ventanas de síntesis (90).
  21. 21. El aparato según cualquiera de las reivindicaciones 6 a 20, en el que la transformada con solapamiento modulada inversa es una transformación de coseno discreta modificada inversa, IMDCT, o una transformación de seno discreta modificada inversa, IMDST.
  22. 22. El aparato según cualquiera de las reivindicaciones 1 a 5, en el que la transformada con solapamiento modulada es una transformación de coseno discreta modificada, MDCT, o una transformación de seno discreta modi ficada, MDST.
  23. 23. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (90) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: -7.078546706512391e-04f, -2.098197727900724e-03f, -4.525198076002370e-03f, -8.233976327300612e-03f, -1.337713096257934e-02f, -1.999721557401502e-02f, -2.800909464274782e-02f, -3.721502082245055e-02f, -4.731768261606175e-02f, -5.794654834034055e-02f, -6.867606753531441e-02f, -7.904647440788692e-02f, -8.859705468085925e-02f, -9.688303623049199e-02f, -1.034961241263523e-01f, -1.080766457616878e-01f, -1.103242262600913e-01f, -1.099809851424550e-01f, -1.068172142230882e-01f, -1.006190418791648e-01f, -9.116452506492527e-02f, -7.820617483254730e-02f, -6.146688124166948e-02f, -4.063362855701623e-02f, -1.536329520788766e-02f, 1.470155068746303e-02f, 4.989736509080558e-02f, 9.050369257152079e-02f, 1.366911019414417e-01f, 1.884686389218322e-01f, 2.456456803467095e-01f, 3.077789078889820e-01f, 3.741642373060188e-01f, 4.438114799213576e-01f, 5.154735456539700e-01f, 5.876661722564289e-01f, 6.587619767809000e-01f, 7.270576699841359e-01f, 7.908752989295335e-01f, 8.486643364959733e-01f, 8.991320235484349e-01f, 9.413348145272842e-01f, 9.747634827941575e-01f, 9.994114730415857e-01f, 1.015760373791603e+00f, 1.024736164069697e+00f, 1.027634294456205e+00f, + 1.025991493983836e+00f, 1.021427210603284e+00f, 1.015439859549357e+00f, 1.009366925499550e+00f, 1.003508162416449e+00f, 9.988898206257559e-01f, 9.953133902427869e-01f, 9.925943919208190e-01f, 9.905771957917731e-01f, 9.891371616557014e-01f, 9.881790747212391e-01f, 9.876249269174586e-01f, 9.874056275509585e-01f, 9.874524849192456e-01f, 9.876951134084213e-01f, 9.880640617030884e-01f, 9.884926873551375e-01f, 9.889230031022089e-01f, 9.893074965384659e-01f, 9.896146331889107e-01f, 9.898319269347060e-01f, 9.899693102025342e-01f, 9.900603352632121e-01f, 9.901575015155720e-01f, 9.903255289051605e-01f, 9.906303787150326e-01f, +9.911298894709990e01f, 9.918665491182922e-01f, 9.928619727154252e-01f, 9.941156069136238e-01f, 9.956033775539884e-01f, 9.972793109558521e-01f, 9.990784840729244e-01f, 1.000922365901945e+00f, + 1.002728111386909e+00f, 1.004416038098237e+00f, 1.005919224127911e+00f, + 1.007189345025525e+00f, 1.008200146369426e+00f, 1.008949493525753e+00f, 1.009458241425143e+00f, 1.009768980817384e+00f, 1.009940336228694e+00f, + 1.010039453539107e+00f, 1.010132323996401e+00f, 1.010272524848519e+00f, + 1.010494354532353e+00f, 1.010808068774316e+00f, 1.011201071127927e+00f, + 1.011641272406023e+00f, 1.012080125934687e+00f, 1.012458183122033e+00f, + 1.012706955800289e+00f, 1.012755013843985e+00f, 1.012530134411619e+00f, 1.011962331100864e+00f, 1.010982135506986e+00f, 1.009512438049510e+00f, + 1.007460860286395e+00f, 1.004708677491086e+00f, 1.001111413242302e+00f, 9.965041017623596e-01f, 9.907199995730845e-01f, 9.823765865983288e-01f, 9.708821747608998e-01f, 9.546732976073705e-01f, 9.321553861564006e-01f, 9.018003682081348e-01f, 8.623984077953557e-01f, 8.132817365236141e-01f, 7.544551974836834e-01f, 6.866580716267418e-01f, 6.113488038789190e-01f, 5.306181649316597e-01f, 4.471309850999502e-01f, 3.639114681156236e-01f, 2.841647033392408e-01f, 2.110209448747969e-01f, 1.472287968327703e-01f, 9.482665349502291e-02f, 5.482436608328477e-02f, 2.701461405056264e-02f, 9.996743588367519e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f
  24. 24. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (90) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: -4.619898752628163e-04f, -9.747166718929050e-04f, -1.664473096973725e-03f, -2.597106916737789e-03f, -3.806285163352241e-03f, -5.324608721716763e-03f, -7.175885277771099e-03f, -9.382480860899108e-03f, -1.195270300743193e-02f, -1.489528159506296e-02f, -1.820666399965468e-02f, -2.187570925786862e-02f, -2.588471937157619e-02f, -3.020862738245264e-02f, -3.481597793538342e-02f, -3.967067992672979e-02f, -4.472698045914417e-02f, -4.994225863256500e-02f, -5.526334794593565e-02f, -6.063717235243996e-02f, -6.600961519440657e-02f, -7.131966266443390e-02f, -7.651178225890490e-02f, -8.152964005319532e-02f, -8.631137544905677e-02f, -9.080411291245728e-02f, -9.495377758870335e-02f, -9.870736514214426e-02f, -1.020202684361974e-01f, -1.048438825017798e-01f, -1.071382314127799e-01f, -1.088690135027248e-01f, -1.099969655786929e-01f, -1.104898474883336e-01f, -1.103225838568563e-01f, -1.094621746650760e-01f, -1.078834293141886e-01f, -1.055612509762041e-01f, -1.024650162703341e-01f, -9.857014566194629e-02f, -9.384684920715425e-02f, -8.826309993000785e-02f, -8.178792716809512e-02f, -7.438785600211463e-02f, -6.602189797715241e-02f, -5.665655641133161e-02f, -4.624456893420224e-02f, -3.474585776145929e-02f, -2.211581608120528e-02f, -8.310425696208936e-03f, 6.717697635290676e-03f, 2.300642061077823e-02f, 4.060106462625085e-02f, 5.953239090915557e-02f, 7.983354189816511e-02f, 1.015233140203748e-01f, 1.246171387327525e-01f, 1.491152519299797e-01f, 1.750067399059861e-01f, 2.022699854906251e-01f, 2.308655379767671e-01f, 2.607365124918583e-01f, 2.918144694729168e-01f, 3.240095704645023e-01f, 3.572175180786021e-01f, 3.913146885756875e-01f, 4.261571642320424e-01f, 4.615925445090212e-01f, 4.974471592901086e-01f, 5.335326819631583e-01f, 5.696546730080154e-01f, 6.056083823929643e-01f, 6.411830842823245e-01f, 6.761653499550255e-01f, 7.103400549562944e-01f, 7.434943718765665e-01f, 7.754281892901473e-01f, 8.059437233154637e-01f, 8.348589373399948e-01f, 8.620108336276733e-01f, 8.872599706865123e-01f, 9.104863121445679e-01f, 9.315962496426278e-01f, 9.505220861927248e-01f, 9.672366712325431e-01f, 9.817397501303696e-01f, 9.940557180662704e-01f, 1.004247514102417e+00f, 1.012407428282884e+00f, 1.018650990561848e+00f, 1.023118841384460e+00f, + 1.025972450969440e+00f, 1.027397523939210e+00f, 1.027585830688143e+00f, + 1.026738673647482e+00f, 1.025061777648234e+00f, 1.022756514615106e+00f, + 1.020009139549275e+00f, 1.016996499560845e+00f, 1.013915946100629e+00f, + 1.011044869639164e+00f, 1.007773858455400e+00f, 1.004848753962734e+00f, 1.002245009135684e+00f, 9.999393169239009e-01f, 9.979055415627330e-01f, 9.961203379971326e-01f, 9.945597525471822e-01f, 9.932031606606762e-01f, 9.920297273323891e-01f, 9.910230654424902e-01f, 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1.011753008569803e+00f, 1.011973876511603e+00f, 1.012182837094955e+00f, + 1.012373028737774e+00f, 1.012535058602453e+00f, 1.012660975529858e+00f, + 1.012740575296603e+00f, 1.012765922449960e+00f, 1.012726958954961e+00f, + 1.012615904116265e+00f, 1.012422888521601e+00f, 1.012140460211194e+00f, + 1.011758810583150e+00f, 1.011269960947744e+00f, 1.010663676735228e+00f, 1.009930754807923e+00f, 1.009058249873833e+00f, 1.008034308295421e+00f, + 1.006843352506855e+00f, 1.005470005637052e+00f, 1.003894772403371e+00f, + 1.002098854400575e+00f, 1.000060686758758e+00f, 9.977600196406868e-01f, 9.951746430061121e-01f, 9.922861082472264e-01f, 9.890757868707590e-01f, 9.847362453480265e-01f, 9.798613526271561e-01f, 9.741378617337759e-01f, 9.673331975559332e-01f, 9.592539757044516e-01f, 9.496984081652284e-01f, 9.384634163826711e-01f, 9.253567968750328e-01f, 9.101986790930605e-01f, 8.928338316495705e 01f, 8.731437835983047e-01f, 8.510420440685049e-01f, 8.264839911291133e-01f, 7.994681492797084e-01f, 7.700431275216928e-01f, 7.383028603058783e-01f, 7.043814340356083e-01f, 6.684616478236647e-01f, 6.307755329382612e-01f, 5.915799587176216e-01f, 5.511703155400274e-01f, 5.098915423728179e-01f, 4.681017110047964e-01f, 4.261772971493010e-01f, 3.845172335531009e-01f, 3.435228672445613e-01f, 3.036004651973099e-01f, 2.651434678028531e-01f, 2.285283969438072e-01f, 1.941021906320984e-01f, 1.621735416384830e-01f, 1.330015240938615e-01f, 1.067840430193724e-01f, 8.365057236623041e-02f, 6.365188111381356e-02f, 4.676538412257621e-02f, 3.288072750732215e-02f, 2.183057564646270e-02f, 1.336381425803019e-02f, 6.758124889697787e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 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0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f
  25. 25. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (90) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: -3.613496418928369e-04f, -7.078546706512391e-04f, -1.074443637110903e-03f, -1.533478537964509e-03f, -2.098197727900724e-03f, -2.778420871815740e-03f, -3.584129920673041e-03f, -4.525198076002370e-03f, -5.609327243712055e-03f, -6.843234536105624e-03f, -8.233976327300612e-03f, -9.785314755557023e-03f, -1.149880303071551e-02f, -1.337713096257934e-02f, -1.542181679511618e-02f, -1.762979910961727e-02f, -1.999721557401502e-02f, -2.252080561390149e-02f, -2.519406300389030e-02f, -2.800909464274782e-02f, -3.095765092956728e-02f, -3.402996266948349e-02f, -3.721502082245055e-02f, -4.050053247568393e-02f, -4.387219218706189e-02f, -4.731768261606175e-02f, -5.082325342672667e-02f, -5.437166635159518e-02f, -5.794654834034055e-02f, -6.153426201732499e-02f, -6.511708163113709e-02f, -6.867606753531441e-02f, -7.219447805250771e-02f, -7.565695975592170e-02f, -7.904647440788692e-02f, -8.234442557322251e-02f, -8.553324579905185e-02f, -8.859705468085925e-02f, -9.152091100798199e-02f, -9.428847446755965e-02f, -9.688303623049198e-02f, -9.929123258537813e-02f, -1.015008467688577e-01f, -1.034961241263523e-01f, -1.052637003544443e-01f, -1.067939984687745e-01f, -1.080766457616878e-01f, -1.090997300590506e-01f, -1.098524491515805e-01f, -1.103242262600913e-01f, -1.105084619148789e-01f, -1.103977408741932e-01f, -1.099809851424550e-01f, -1.092492774392824e-01f, -1.081974227416502e-01f, -1.068172142230882e-01f, -1.050995803285455e-01f, -1.030360111111103e-01f, -1.006190418791648e-01f, -9.784120023411771e-02f, -9.469304216883027e-02f, -9.116452506492527e-02f, -8.724644532866996e-02f, -8.293043914044632e-02f, -7.820617483254730e-02f, -7.306142427456862e-02f, -6.748468182105991e-02f, -6.146688124166948e-02f, -5.499497258200362e-02f, -4.805444424454820e-02f, 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7.047092819314779e-01f, 7.270576699841359e-01f, 7.489068963384272e-01f, 7.701990187606995e-01f, 7.908752989295335e-01f, 8.108788692151807e-01f, 8.301579139160681e-01f, 8.486643364959733e-01f, 8.663548164329093e-01f, 8.831896853053627e-01f, 8.991320235484349e-01f, 9.141540563656075e-01f, 9.282282546151819e-01f, 9.413348145272842e-01f, 9.534619388400459e-01f, 9.646048250501910e-01f, 9.747634827941575e-01f, 9.839435385219192e-01f, 9.921529097154242e-01f, 9.994114730415857e-01f, 1.005746084650236e+00f, 1.011183971347815e+00f, 1.015760373791603e+00f, 1.019515072412387e+00f, + 1.022490937034641e+00f, 1.024736164069697e+00f, 1.026304095700693e+00f, + 1.027250978292214e+00f, 1.027634294456205e+00f, 1.027511063644843e+00f, 1.026942795115598e+00f, 1.025991493983836e+00f, 1.024716149969084e+00f, + 1.023175976163407e+00f, 1.021427210603284e+00f, 1.019521566634239e+00f, 1.017510118327508e+00f, 1.015439859549357e+00f, 1.013460916839174e+00f, 1.011654901040475e+00f, 1.009366925499550e+00f, 1.007263182132894e+00f, 1.005313192386866e+00f, + 1.003508162416449e+00f, 1.001840787319378e+00f, 1.000303927234380e+00f, 9.988898206257559e-01f, 9.975915283480670e-01f, 9.964015284765968e-01f, 9.953133902427869e-01f, 9.943201078053212e-01f, 9.934158959186011e-01f, 9.925943919208190e-01f, 9.918510277326026e-01f, 9.911797988363887e-01f, 9.905771957917731e-01f, 9.900381047643838e-01f, 9.895594394179152e-01f, 9.891371616557014e-01f, 9.887684373604154e-01f, 9.884497924570929e-01f, 9.881790747212391e-01f, 9.879528358230726e-01f, 9.877691368590689e-01f, 9.876249269174586e-01f, 9.875179947346887e-01f, 9.874458127312921e-01f, 9.874056275509585e-01f, 9.873951115886979e-01f, 9.874115368168944e-01f, 9.874524849192456e-01f, 9.875149888347144e-01f, 9.875968894760857e-01f, 9.876951134084213e-01f, 9.878075819424549e-01f, 9.879311998177238e-01f, 9.880640617030884e-01f, 9.882032571565917e-01f, 9.883471084085503e-01f, 9.884926873551375e-01f, 9.886386592120545e-01f, 9.887825578295630e-01f, 9.889230031022089e-01f, 9.890581715933395e-01f, 9.891867674284610e-01f, 9.893074965384659e-01f, 9.894196399062921e-01f, 9.895220757174378e-01f, 9.896146331889107e-01f, 9.896970346678272e-01f, 9.897692596535289e-01f, 9.898319269347060e-01f, 9.898852572653667e-01f, 9.899307640365727e-01f, 9.899693102025343e-01f, 9.900025692522435e-01f, 9.900321562263099e-01f, 9.900603352632121e-01f, 9.900889812894406e-01f, 9.901206586012907e-01f, 9.901575015155720e-01f, 9.902023946214220e-01f, 9.902575406142213e-01f, 9.903255289051605e-01f, 9.904087914462694e-01f, 9.905096491583045e-01f, 9.906303787150326e-01f, 9.907727108894024e-01f, 9.909387444078919e-01f, 9.911298894709990e-01f, 9.913476318763218e-01f, 9.915928560402563e-01f, 9.918665491182922e-01f, 9.921691315380984e-01f, 9.925010851461232e-01f, 9.928619727154252e-01f, 9.932519181564613e-01f, 9.936700207375173e-01f, 9.941156069136238e-01f, 9.945873147903244e-01f, 9.950837402063278e-01f, 9.956033775539884e-01f, 9.961439922621166e-01f, 9.967034533921340e-01f, 9.972793109558521e-01f, 9.978690858367024e-01f, 9.984697087896268e-01f, 9.990784840729244e-01f, 9.996919011206490e-01f, 1.000308193833526e+00f, + 1.000922365901945e+00f, 1.001532636590676e+00f, 1.002135464655177e+00f, + 1.002728111386909e+00f, 1.003307449770187e+00f, 1.003870934089686e+00f, + 1.004416038098237e+00f, 1.004940548815171e+00f, 1.005442141810160e+00f, + 1.005919224127911e+00f, 1.006370303149314e+00f, 1.006793927824538e+00f, 1.007189345025525e+00f, 1.007555573455895e+00f, 1.007892674961336e+00f, + 1.008200146369426e+00f, 1.008478423284851e+00f, 1.008727884997619e+00f, + 1.008949493525753e+00f, 1.009144112734761e+00f, 1.009313224929575e+00f, + 1.009458241425143e+00f, 1.009581280555682e+00f, 1.009684090687164e+00f, + 1.009768980817384e+00f, 1.009838308708799e+00f, 1.009894548257807e+00f, + 1.009940336228694e+00f, 1.009977916643680e+00f, 1.010010230290263e+00f, + 1.010039453539107e+00f, 1.010068202038694e+00f, 1.010098388689342e+00f, + 1.010132323996401e+00f, 1.010171656775640e+00f, 1.010218096148412e+00f, + 1.010272524848519e+00f, 1.010336490294771e+00f, 1.010410221483215e+00f, + 1.010494354532353e+00f, 1.010588873699422e+00f, 1.010693501186928e+00f, + 1.010808068774316e+00f, 1.010931436739342e+00f, 1.011062876503041e+00f, + 1.011201071127927e+00f, 1.011344700694417e+00f, 1.011491904228184e+00f, + 1.011641272406023e+00f, 1.011790282474963e+00f, 1.011937567254485e+00f, + 1.012080125934687e+00f, 1.012216235487353e+00f, 1.012342907951334e+00f, + 1.012458183122033e+00f, 1.012558879696851e+00f, 1.012642857380847e+00f, + 1.012706955800289e+00f, 1.012748952907404e+00f, 1.012765799894453e+00f, + 1.012755013843985e+00f, 1.012713798678211e+00f, 1.012639775003457e+00f, + 1.012530134411619e+00f, 1.012382309473470e+00f, 1.012194068117524e+00f, + 1.011962331100864e+00f, 1.011685173724601e+00f, 1.011359143572147e+00f, + 1.010982135506986e+00f, 1.010550715971368e+00f, 1.010062133151922e+00f, + 1.009512438049510e+00f, 1.008898689394160e+00f, 1.008215923600973e+00f, + 1.007460860286395e+00f, 1.006627741823389e+00f, 1.005712337656749e+00f, + 1.004708677491086e+00f, 1.003611467285588e+00f, 1.002414286392268e+00f, + 1.001111413242302e+00f, 9.996961651093181e-01f, 9.981625949525345e-01f, 9.965041017623596e-01f, 9.947148884277037e-01f, 9.927891912841345e-01f, 9.907199995730845e-01f, 9.884793707533194e-01f, 9.855347660016696e-01f, 9.823765865983286e-01f, 9.789747333404933e-01f, 9.751623811486372e-01f, 9.708821747608998e-01f, 9.660805524695870e-01f, 9.606976399184645e-01f, 9.546732976073706e-01f, 9.479479345282376e-01f, 9.404609052933396e-01f, 9.321553861564006e-01f, 9.229775478442888e-01f, 9.128745354570823e-01f, 9.018003682081348e-01f, 8.897163275605041e-01f, 8.765908974996186e-01f, 8.623984077953557e-01f, 8.471200801854385e-01f, 8.307479727020245e-01f, 8.132817365236141e-01f, 7.947291447585267e-01f, 7.751108841891807e-01f, 7.544551974836834e-01f, 7.327963552921717e-01f, 7.101790843209148e-01f, 6.866580716267418e-01f, 6.622962432368731e-01f, 6.371684119604742e-01f, 6.113488038789190e-01f, 5.849206604934815e-01f, 5.579747428663487e-01f, 5.306181649316717e-01f, 5.029523957059122e-01f, 4.750868825511614e-01f, 4.471309850999535e-01f, 4.192049917945288e-01f, 3.914252910998820e-01f, 3.639114681156252e-01f, 3.367837772954476e-01f, 3.101627843160973e-01f, 2.841647033392418e-01f, 2.589033711808454e-01f, 2.344880603710975e-01f, 2.110209448747974e-01f, 1.885997642296488e-01f, 1.673100807904834e-01f, 1.472287968327706e-01f, 1.284223074167396e-01f, 1.109422548710344e-01f, 9.482665349502306e-02f, 8.009914366829558e-02f, 6.676765847398403e-02f, 5.482436608328485e-02f, 4.424588851571281e-02f, 3.499361000717621e-02f, 2.701461405056267e-02f, 2.024370180670145e-02f, 1.460796755137538e-02f, 9.996743588367531e-03f, 5.305235098871444e-03f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 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0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, +0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f, 0.000000000000000e+00f
  26. 26. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (90) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: -3.021153494057143e-04f, - 5.867737487939294e-04f, -8.366504004139796e-04f, ■1.126635355725494e-03f, -1.470492941694331e-03f, - 1.873473391018495e-03f, -2.339292362082021e-03f, ■2.872008069419264e-03f, -3.476256385086407e-03f, - 4.155963816705528e-03f, -4.914563787665504e-03f, 5.755172503953251e-03f, -6.680623380533122e-03f, - 7.693816924650567e-03f, -8.796760749750191e-03f, 9.990503073705982e-03f, -1.127574117138621e-02f, - 1.265334152129685e-02f, -1.412438986522702e-02f, 1.568889620430290e-02f, -1.734512089366117e-02f, - 1.909097368362797e-02f, -2.092546711168754e-02f, 2.284684792818856e-02f, -2.485207716234951e-02f, - 2.693746704328349e-02f, -2.909952486193999e-02f, 3.133504629493832e-02f, -3.363960728361352e-02f, - 3.600820974457969e-02f, -3.843601741746971e-02f, 4.091746034850161e-02f, -4.344654894948344e-02f, - 4.601786724624048e-02f, 4.862598509282497e-02f, 5.126474204655663e-02f, -5.392644753556616e-02f, - 5.660384311081047e-02f, ■5.929116747072080e-02f, 6.198268202511926e-02f, -6.467025548071184e-02f, - 6.734542216184526e-02f, -7.000099017198280e-02f, 7.263057011354321e-02f, -7.522784961377151e-02f, - 7.778525942347714e-02f, -8.029480247839878e-02f, ■8.274924535373614e-02f, -8.514125464087215e-02f, - 8.746379123238275e-02f, -8.971069341834263e-02f, 9.187564084638347e-02f, -9.395176975347193e-02f, - 9.593137735886889e-02f, -9.780843257659243e-02f, 9.957851303827886e-02f, -1.012361165314596e-01f, - 1.027741036495644e-01f, -1.041861222641119e-01f, 1.054680247057000e-01f, -1.066160875985523e-01f, - 1.076255384835563e-01f, -1.084912299471198e-01f, 1.092087422379003e-01f, -1.097736146613313e-01f, - 1.101808861640070e-01f, -1.104271876052675e-01f, 1.105108362290460e-01f, -1.104281465492726e-01f, - 1.101739218186236e-01f, 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  27. 27. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (90) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: -2.353032150516754e-04f, -4.619898752628163e-04f, -6.262931535610879e-04f, 7.929180432976445e-04f, -9.747166718929050e-04f, -1.180256894474562e-03f, -1.409209039594871e-03f, 1.664473096973725e-03f, -1.946591608170231e-03f, -2.257081732588478e-03f, -2.597106916737789e-03f, 2.967607624839524e-03f, -3.370454877988472e-03f, -3.806285163352241e-03f, -4.276873767639064e-03f, 4.782469904501813e-03f, -5.324608721716763e-03f, -5.903403814095400e-03f, -6.520419726599805e-03f, ■7.175885277771099e-03f, -7.871422820642307e-03f, -8.606586039759667e-03f, -9.382480860899108e-03f, 1.019827182163307e-02f, -1.105520547739066e-02f, -1.195270300743193e-02f, -1.289205910303846e-02f, 1.387263484323160e-02f, -1.489528159506296e-02f, -1.595856621933800e-02f, 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  28. 28. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (90) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: -1.596869453315999e-04, -3.021153494057143e-04, -4.142323860121641e-04, -5.058484031439142e-04, -5.867737487939294e-04, -6.666034929771656e-04, -7.499813122143762e-04, -8.366504004139794e-04, -9.273096237893370e-04, -1.023773491532728e-03, -1.126635355725494e-03, -1.235247794937702e-03, -1.349627853510606e-03, -1.470492941694331e-03, -1.598145399394582e-03, -1.732450700747454e-03, -1.873473391018495e-03, -2.021493133113876e-03, -2.176721793926887e-03, -2.339292362082021e-03, -2.509298051958086e-03, -2.686801873698675e-03, -2.872008069419264e-03, -3.065254982136409e-03, -3.266686736002951e-03, -3.476256385086407e-03, -3.694123506258334e-03, -3.920651988943251e-03, -4.155963816705528e-03, -4.399940204176431e-03, -4.652692827862344e-03, 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-2.417463749934085e-02, -2.485207716234951e-02, -2.553826580898371e-02, -2.623344061522424e-02, -2.693746704328349e-02, -2.764983997782559e-02, -2.837043858580717e-02, -2.909952486193998e-02, -2.983695676902939e-02, -3.058218787751172e-02, -3.133504629493832e-02, -3.209573641742117e-02, -3.286409853195186e-02, -3.363960728361352e-02, -3.442207835192332e-02, -3.521166997276568e-02, -3.600820974457969e-02, -3.681119317395579e-02, -3.762042487257546e-02, -3.843601741746971e-02, -3.925772507976759e-02, -4.008494689009130e-02, -4.091746034850161e-02, -4.175542154425013e-02, -4.259863408038441e-02, -4.344654894948344e-02, -4.429899287523113e-02, -4.515616616948602e-02, -4.601786724624048e-02, -4.688349274164030e-02, -4.775281564045485e-02, -4.862598509282498e-02, -4.950274425624717e-02, -5.038242975874127e-02, -5.126474204655663e-02, -5.214974857230398e-02, -5.303718358615044e-02, -5.392644753556616e-02, -5.481729406855359e-02, -5.570983057565210e-02, -5.660384311081047e-02, -5.749879655200370e-02, -5.839451321393058e-02, -5.929116747072080e-02, -6.018848884279070e-02, -6.108576415855094e-02, -6.198268202511926e-02, -6.287933502598060e-02, -6.377542359879805e-02, -6.467025548071184e-02, -6.556352962710620e-02, -6.645533804325808e-02, -6.734542216184526e-02, -6.823317113969737e-02, -6.911832800881393e-02, -7.000099017198280e-02, -7.088091415536939e-02, -7.175751581450866e-02, -7.263057011354321e-02, -7.350020923324756e-02, -7.436618116832702e-02, -7.522784961377151e-02, -7.608493286734087e-02, -7.693750413779520e-02, -7.778525942347714e-02, -7.862751920094575e-02, -7.946399769633587e-02, -8.029480247839879e-02, -8.111965623403654e-02, -8.193789640255647e-02, -8.274924535373614e-02, -8.355381170261278e-02, -8.435134905678848e-02, -8.514125464087215e-02, -8.592328028689659e-02, -8.669753354886602e-02, -8.746379123238275e-02, -8.822149831804039e-02, -8.897043074644968e-02, -8.971069341834263e-02, -9.044201341183719e-02, -9.116374329727489e-02, -9.187564084638347e-02, -9.257786640497777e-02, -9.327014538321736e-02, -9.395176975347193e-02, -9.462246851310178e-02, -9.528240981433814e-02, -9.593137735886889e-02, -9.656876884228789e-02, -9.719438533739366e-02, -9.780843257659243e-02, -9.841075978146442e-02, -9.900085534600200e-02, -9.957851303827886e-02, -1.001438325530028e-01, -1.006965654660066e-01, -1.012361165314596e-01, -1.017622262660318e-01, -1.022749718234132e-01, -1.027741036495644e-01, -1.032590485916072e-01, -1.037296416381658e-01, -1.041861222641119e-01, -1.046283222746241e-01, -1.050556674062305e-01, -1.054680247057000e-01, -1.058657014776354e-01, -1.062485747526411e-01, -1.066160875985523e-01, -1.069680384993124e-01, -1.073045851468520e-01, -1.076255384835563e-01, -1.079303623240916e-01 1.082188709931267e-01 -1.084912299471198e-01, -1.087472718159103e-01, -1.089864959432877e-01 1.092087422379003e-01 -1.094141900597718e-01, -1.096026598727515e-01, -1.097736146613313e-01 1.099268894481712e-01 -1.100626919008929e-01, 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-9.670445315437526e-02, -9.591769653314886e-02, -9.510723623306666e-02 9.427290387369003e-02 -9.341489003828900e-02, -9.253303383231506e-02, -9.162682426346705e-02 9.069614104466586e-02 -8.974125216128212e-02, -8.876201954716677e-02, -8.775790063882420e-02 8.672877689119252e-02 -8.567495161533510e-02, -8.459627389188201e-02, -8.349213839083708e-02 8.236235749389448e-02 -8.120716401834208e-02, -8.002639902061687e-02, -7.881950797067065e-02 7.758626878445929e-02 -7.632679536516856e-02, -7.504088747769501e-02, -7.372803129789816e-02 7.238806162166744e-02 -7.102116211954443e-02, -6.962720872934396e-02, -6.820576796149519e-02 6.675671622392269e-02 -6.528023606863240e-02, -6.377611429172260e-02, -6.224374611498080e-02 6.068292908100376e-02 -5.909386001558149e-02, -5.747627430502456e-02, -5.582945016301614e-02 5.415316322402774e-02 -5.244768784057990e-02, -5.071287102956145e-02, -4.894812724598650e-02 4.715324945932696e-02 -4.532841381541464e-02, -4.347347112195197e-02, -4.158794238398249e-02 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7.462862199422061-02 7.808896236959446e-02 8.158769578329894e-02, 8.512490568723846e-02 8.870101069974845e-02 , 9.231608110264714e-02 , 9.596983987496970e-02 9.966236893806717e-02 1.033941063338643e-01 , 1.071650779014335e-01 , 1.109748994439795e-01 1.148235927259266e-01 1.187115850305241e-01 , 1.226388834300689e-01 , 1.266050731283809e-01 1.306101067250375e-01 1.346543064817742e-01 , 1.387376249190578e-01 , 1.428596447589721e-01 1.470203170721216e-01 1.512199592605080e-01 , 1.554584725339102e-01 , 1.597353438179875e-01 1.640504702561671e-01 1.684041609371527e-01 , 1.727963503982179e-01 , 1.772265953627290e-01 1.816947894623263e-01 1.862011624788949e-01 , 1.907455489457267e-01 , 1.953273880886783e-01 1.999464539304762e-01 2.046028558464008e-01 , 2.092963206850239e-01 , 2.140261955702662e-01 2.187922274259156e-01 2.235945635254679e-01 , 2.284329840640989e-01 , 2.333068981094213e-01 2.382160219461597e-01 2.431603785542250e-01 , 2.481396077816722e-01 , 2.531529721334063e-01 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0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
  29. 29. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +9.959086585790517e-04, 3.819056787237678e-03, 9.540832613229890e-03, 1.921659800166160e-02, 3.382719081038548e-02, 5.424831667522354e-02, 8.120777668775610e-02, 1.152171887125930e-01, 1.564942331034909e-01, 2.049363422022628e-01, 2.601166575816199e-01, 3.212814164616093e-01, 3.873472997948746e-01, 4.569497078592333e-01, 5.285192958868393e-01, 6.003522489375573e-01, 6.706896380227332e-01, 7.378044458510402e-01, 8.000925313431716e-01, 8.561409184410547e-01, 9.048272294524792e-01, 9.453685031730190e-01, 9.773507430600533e-01, 1.000800872826561e+00, 1.016171590112097e+00, 1.024315247630982e+00, 1.026415431432931e+00, 1.023858366571912e+00, 1.018135705524407e+00, 1.010794822557756e+00, 1.003406509762925e+00, 9.967831265986109e-01, 9.920995520917141e-01, 9.892206942816891e-01, 9.879658322200813e-01, 9.881273531631907e-01, 9.894805541465801e-01, 9.917849916000535e-01, 9.947847580943504e-01, 9.982119669301160e-01, 1.001791235858836e+00, 1.005242583245485e+00, 1.008283053756130e+00, 1.010631281038659e+00, 1.012015300253356e+00, 1.012180753005270e+00, 1.010896765282633e+00, 1.007963362035220e+00, 1.003227255072391e+00, 9.966050551498514e-01, 9.868284225039941e-01, 9.731250287581631e-01, 9.540636479502398e-01, 9.283864275822276e-01, 8.950916858157935e-01, 8.534769362643825e-01, 8.032090930429980e-01, 7.444735201251689e-01, 6.780787033699449e-01, 6.053970453856138e-01, 5.282077505750667e-01, 4.486552956056635e-01, 3.691875990296312e-01, 2.924566408966777e-01, +2.210718537110463e-01, 1.573148583944309e-01, 1.030525757797768e-01, 5.982732244758054e-02, 2.871831923385133e-02, 9.683884928956490e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
  30. 30. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +6.143388180964179e-04, 1.489582832987000e-03, 2.884104959764029e-03, 4.934298832466617e-03, 7.779130464154915e-03, 1.154910606525086e-02, 1.637155619860352e-02, 2.237116158648752e-02, 2.966159685753317e-02, 3.835663329277230e-02, 4.855610986150206e-02, 6.035055738891727e-02, 7.382288203064732e-02, 8.903563687211119e-02, 1.060356225286319e-01, 1.248534855777947e-01, 1.454931890869180e-01, 1.679435556337752e-01, 1.921728622634411e-01, 2.181238261985594e-01, 2.457259744642953e-01, 2.748839432649996e-01, 3.054824712370942e-01, 3.373873799614014e-01, 3.704415932452488e-01, 4.044749630814483e-01, 4.393004362003260e-01, 4.747225454237193e-01, 5.105341492548225e-01, 5.465201916422433e-01, 5.824658100332457e-01, 6.181452662624718e-01, 6.533411462740817e-01, 6.878367295965062e-01, 7.214176027060971e-01, 7.538887973483771e-01, 7.850546571907628e-01, 8.147397447696774e-01, 8.427819363777799e-01, 8.690376742017057e-01, 8.933935477349644e-01, 9.157483563218768e-01, 9.360270196617569e-01, 9.541731142261065e-01, 9.701635474343885e-01, 9.840036439809510e-01, 9.957199420334376e-01, 1.005374268639838e+00, 1.013046655758663e+00, 1.018843380560658e+00, 1.022896948293643e+00, 1.025355286710874e+00, 1.026382881625701e+00, 1.026155530733488e+00, 1.024853974580724e+00, 1.022664602721801e+00, 1.019779396547454e+00, 1.016391686789653e+00, 1.012697033320358e+00, 1.008885191761748e+00, 1.005378742804807e+00, 1.001563778373068e+00, 9.982531564931281e-01, 9.954346644968789e-01, 9.930950268060122e-01, 9.912170911359961e-01, 9.897805192546195e-01, 9.887624937408933e-01, 9.881383235740961e-01, 9.878819413827574e-01, 9.879662130250981e-01, 9.883630508181326e-01, 9.890434070785485e-01, 9.899772316163624e-01, 9.911334564321237e-01, 9.924800441092685e-01, 9.939841207305906e-01, 9.956121471675398e-01, 9.973300590248015e-01, 9.991033633647473e-01, 1.000897441314013e+00, 1.002677088643863e+00, 1.004407190937699e+00, 1.006052289109999e+00, 1.007576934100958e+00, 1.008945862447015e+00, 1.010124241309341e+00, 1.011077969726137e+00, 1.011773962181442e+00, 1.012180362866919e+00, 1.012266707295288e+00, 1.012004064757857e+00, 1.011365223023975e+00, 1.010324996851905e+00, 1.008860731864438e+00, 1.006952983357691e+00, 1.004586273379809e+00, 1.001749900308864e+00, 9.984386632116344e-01, 9.946500332901397e-01, 9.895756853352172e-01, 9.838303127859196e-01, 9.769999155793757e-01, 9.689141159310996e-01, 9.594038121639412e-01, 9.483086322505029e-01, 9.354860218216989e-01, 9.208101305030523e-01, 9.041732260327581e-01, 8.854882249661838e-01, 8.646864947605046e-01, 8.417237467711145e-01, 8.165875713256009e-01, 7.892986353718001e-01, 7.599171886893816e-01, 7.285474515411827e-01, 6.953282935906302e-01, 6.604334017809461e-01, 6.240661431421666e-01, 5.864461424698465e-01, 5.478160663871147e-01, 5.084499758302218e-01, 4.686361426418982e-01, 4.286789889246253e-01, 3.889032719013045e-01, 3.496431418636314e-01, 3.112360816586544e-01, 2.740128472224535e-01, 2.382847225401666e-01, 2.043379825955252e-01, 1.724305860483632e-01, 1.427939789949265e-01, 1.156385879569741e-01, 9.115821766571995e-02, 6.952749039054593e-02, 5.088975408628225e-02, 3.533430192568954e-02, 2.286680405144430e-02, 1.338005016725895e-02, 6.640506529168652e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00
  31. 31. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +5.087227626168386e-04, 9.959086585790517e-04, 1.682208006328800e-03, 2.609697259047744e-03, 3.819056787237678e-03, 5.349319592933909e-03, 7.243906383895192e-03, 9.540832613229890e-03, 1.227637642543709e-02, 1.548950238899404e-02, 1.921659800166160e-02, 2.349369619441617e-02, 2.835199581667961e-02, 3.382719081038548e-02, 3.994939538719628e-02, 4.674775238543380e-02, 5.424831667522354e-02, 6.247770776443612e-02, 7.145835917501348e-02, 8.120777668775610e-02, 9.174400412319896e-02, 1.030764959637497e-01, 1.152171887125930e-01, 1.281665713944242e-01, 1.419264381068653e-01, 1.564942331034909e-01, 1.718593189799504e-01, 1.880134254543744e-01, 2.049363422022628e-01, 2.226123055761096e-01, 2.410151242797736e-01, 2.601166575816199e-01, 2.798871008989962e-01, 3.002880135563586e-01, 3.212814164616093e-01, 3.428208463088390e-01, 3.648596557863134e-01, 3.873472997948746e-01, 4.102294951869188e-01, 4.334494534591082e-01, 4.569497078592333e-01, 4.806696403251166e-01, 5.045473815014847e-01, 5.285192958868393e-01, +5.525196099932443e-01, 5.764872452085427e-01, 6.003522489375573e-01, 6.240509872809882e-01, 6.475182586093196e-01, 6.706896380227332e-01, 6.935029068990036e-01, 7.158927516396895e-01, 7.378044458510402e-01, 7.591787241845952e-01, 7.799586608897265e-01, 8.000925313431716e-01, 8.195318652294690e-01, 8.382288957404715e-01, 8.561409184410547e-01, 8.732316951214179e-01, 8.894702022170831e-01, 9.048272294524792e-01, 9.192736375782965e-01, 9.327940405054362e-01, 9.453685031730190e-01, 9.569883933538136e-01, 9.676486424195593e-01, 9.773507430600533e-01, 9.861027831072527e-01, 9.939122412655677e-01, 1.000800872826561e+00, 1.006787811971719e+00, 1.011901269172423e+00, 1.016171590112097e+00, 1.019636414864842e+00, 1.022336613864005e+00, 1.024315247630982e+00, 1.025621299895396e+00, 1.026303439275662e+00, 1.026415431432931e+00, 1.026007933174836e+00, 1.025137435167917e+00, 1.023858366571912e+00, 1.022226936424625e+00, 1.020300550334848e+00, 1.018135705524407e+00, 1.015792146756340e+00, 1.013325966774524e+00, 1.010794822557756e+00, 1.008265131568879e+00, 1.006046874304407e+00, 1.003406509762925e+00, 1.000977398831985e+00, 9.987704535700208e-01, 9.967831265986109e-01, 9.950118905889862e-01, 9.934523971504882e-01, 9.920995520917141e-01, 9.909475998606236e-01, 9.899902426925508e-01, 9.892206942816891e-01, 9.886318043013834e-01, 9.882160904669929e-01, 9.879658322200813e-01, 9.878730767519871e-01, 9.879296932443894e-01, 9.881273531631907e-01, 9.884575535474619e-01, 9.889115869213529e-01, 9.894805541465801e-01, 9.901553455166457e-01, 9.909266562913843e-01, 9.917849916000535e-01, 9.927206838643636e-01, 9.937239208721489e-01, 9.947847580943504e-01, 9.958931493776203e-01, 9.970389567617592e-01, 9.982119669301160e-01, 9.994020338838508e-01, 1.000598323893564e+00, 1.001791235858836e+00, 1.002969837054169e+00, 1.004123786397111e+00, 1.005242583245485e+00, 1.006315717067918e+00, 1.007332693127034e+00, 1.008283053756130e+00, 1.009156423082384e+00, 1.009942535308151e+00, 1.010631281038659e+00, 1.011212744622770e+00, 1.011677230257499e+00, 1.012015300253356e+00, 1.012217779097186e+00, 1.012275790821109e+00, 1.012180753005270e+00, 1.011924425888915e+00, 1.011498917644724e+00, 1.010896765282633e+00, 1.010110965619444e+00, 1.009135094671655e+00, 1.007963362035220e+00, 1.006590756505588e+00, 1.005013115379014e+00, 1.003227255072391e+00, 1.001231060075500e+00, 9.990235555436858e-01, 9.966050551498514e-01, 9.939894706113089e-01, 9.904539200261149e-01, 9.868284225039941e-01 9.827716736909488e-01, 9.782206672373213e-01, 9.731250287581631e-01, 9.674323528812744e-01, 9.610947043524248e-01, 9.540636479502398e-01, 9.462952991190324e-01, 9.377489107516087e-01, 9.283864275822276e-01, 9.181762606422500e-01, 9.070861558801854e-01, 8.950916858157935e-01, 8.821696237804294e-01, 8.683025287048570e-01, 8.534769362643825e-01, 8.376852006833730e-01, 8.209275259764013e-01, 8.032090930429980e-01, 7.845450482523652e-01, 7.649554851899686e-01, 7.444735201251689e-01, 7.231348066419057e-01, 7.009860555207412e-01, 6.780787033699450e-01, 6.544686506489734e-01, 6.302212149502727e-01, 6.053970453856138e-01, 5.800715766089168e-01, 5.543129276657669e-01, 5.282077505750727e-01, 5.018369724442092e-01, 4.752902962082383e-01, 4.486552956056652e-01, 4.220281118338883e-01, 3.955057965950340e-01, 3.691875990296320e-01, 3.431732847389720e-01, 3.175633015043183e-01, 2.924566408966782e-01, 2.679463783886042e-01, 2.441231331518492e-01, 2.210718537110466e-01, 1.988719153219592e-01, 1.775967625327044e-01, 1.573148583944310e-01, 1.380903364946733e-01, 1.199837497591550e-01, 1.030525757797769e-01, 8.735085011789188e-02, 7.292811584897502e-02, 5.982732244758056e-02, 4.808178837444506e-02, 3.771135297837851e-02, 2.871831923385135e-02, 2.108352028641225e-02, 1.476289412849005e-02, 9.683884928956495e-03, 5.642168789286858e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00
  32. 32. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +4.595886345493055e-04, 7.919323614002698e-04, 1.227927169310031e-03, 1.783653266717233e-03, 2.479549413444207e-03, 3.329799454594261e-03, 4.353535478916468e-03, 5.564965156664018e-03, 6.986108359341676e-03, 8.629882322202329e-03, 1.051343406844975e-02, 1.265082642578719e-02, 1.506090447446532e-02, 1.775591229287213e-02, 2.075475983187825e-02, 2.406813715401559e-02, 2.771207863541604e-02, 3.169933248543932e-02, 3.604609640533871e-02, 4.076128638095439e-02, 4.586038120884381e-02, 5.135136676471998e-02, 5.724780220726930e-02, 6.355854744461048e-02, 7.029450733434550e-02, 7.745987198268531e-02, 8.506635369887924e-02, 9.311641620512773e-02, 1.016162955027316e-01, 1.105690806271684e-01, 1.199789286645804e-01, 1.298417294090302e-01, 1.401623800497866e-01, 1.509371564593891e-01, 1.621632295622287e-01, 1.738354123649302e-01, 1.859520359191026e-01, 1.985008828937603e-01, 2.114778554475382e-01, 2.248732557074316e-01, 2.386763947872762e-01, 2.528729453658238e-01, 2.674547009618951e-01, 2.824031465430401e-01, +2.977050145264297e-01, 3.133419120661713e-01, 3.292976696294886e-01, 3.455490160824131e-01, 3.620795045342974e-01, 3.788648665671841e-01, 3.958851576591690e-01, 4.131143794748322e-01, 4.305308301005456e-01, 4.481076715576617e-01, 4.658227790464821e-01, 4.836466393241829e-01, 5.015564851667653e-01, 5.195228071176610e-01, 5.375197039843709e-01, 5.555183841040963e-01, 5.734957812557457e-01, 5.914186654649489e-01, 6.092622887527459e-01, 6.269981160888640e-01, 6.446002007776794e-01, 6.620384583071039e-01, 6.792906550106088e-01, 6.963256426589250e-01, 7.131194393772130e-01, 7.296469905863920e-01, 7.458864594794676e-01, 7.618094719403713e-01, 7.773958448163656e-01, 7.926208751337592e-01, 8.074666387233143e-01, 8.219101564897180e-01, 8.359343163788637e-01, 8.495180470826319e-01, 8.626485837105826e-01, 8.753083234662220e-01, 8.874884715160425e-01, 8.991737724042251e-01, 9.103527429187326e-01, 9.210144133066616e-01, 9.311556192776946e-01, 9.407644740241826e-01, 9.498382236872068e-01, 9.583732599601223e-01, 9.663690412284377e-01, 9.738235617865406e-01, 9.807442506043361e-01, 9.871297972052695e-01, 9.929872268444632e-01, 9.983241398929388e-01, 1.003150760219063e+00, 1.007473713377193e+00, 1.011309151636166e+00, 1.014666681083198e+00, 1.017563337333301e+00, 1.020014681326785e+00, 1.022039872150903e+00, 1.023654257342442e+00, 1.024881624147540e+00, 1.025739288978437e+00, 1.026250709375593e+00, 1.026436666375082e+00, 1.026320857404224e+00, 1.025922917798664e+00, 1.025269979527211e+00, 1.024382188798244e+00, 1.023284940887058e+00, 1.022000829220643e+00, 1.020555973231408e+00, 1.018971390778550e+00, 1.017275179369116e+00, 1.015489129111694e+00, 1.013639356938881e+00, 1.011747750709711e+00, 1.009840844244693e+00, 1.007939764480188e+00, 1.006407400915498e+00, 1.004374825095777e+00, 1.002469814737132e+00, 1.000689073754539e+00, 9.990346001249977e-01, 9.975024904153303e-01, 9.960941547576162e-01, 9.948051243621099e-01, 9.936362728142866e-01, 9.925826537087717e-01, 9.916447007525191e-01, 9.908170758245324e-01, 9.900998445795673e-01, 9.894873685512386e-01, 9.889794323427195e-01, 9.885701787626714e-01, 9.882591911282058e-01, 9.880404423341358e-01, 9.879133688360181e-01, 9.878718098237022e-01, 9.879150762106034e-01, 9.880368938846610e-01, 9.882364564839506e-01, 9.885073687439192e-01, 9.888487088987707e-01, 9.892539488627546e-01, 9.897220412447528e-01, 9.902463287269285e-01, 9.908256340476208e-01, 9.914531811725067e-01, 9.921276814881759e-01, 9.928422499725458e-01, 9.935955098307742e-01, 9.943804814776256e-01, 9.951957244449919e-01, 9.960341878404958e-01, 9.968943831870675e-01, 9.977692009836100e-01, 9.986571134591464e-01, 9.995509738170480e-01, 1.000449227898040e+00, 1.001344692310058e+00, 1.002235786606954e+00, 1.003115291715261e+00, 1.003981602446902e+00, 1.004827468041713e+00, 1.005651275972376e+00, 1.006445772052972e+00, 1.007209352772459e+00, 1.007934783656087e+00, 1.008620496650569e+00, 1.009259314290145e+00, 1.009849742422788e+00, 1.010384692193296e+00, 1.010862783160582e+00, 1.011277044709547e+00, 1.011626247430694e+00, 1.011903571699736e+00, 1.012107954864219e+00, 1.012232755709885e+00, 1.012277089047072e+00, 1.012234505114778e+00, 1.012104319978655e+00, 1.011880293122688e+00, 1.011561972516341e+00, 1.011143373963981e+00, 1.010624321020038e+00, 1.009999148545101e+00, 1.009268031808824e+00, 1.008425698479647e+00, 1.007472774447058e+00, 1.006404483571931e+00, 1.005222003295591e+00, 1.003921160689206e+00, 1.002503762756151e+00, 1.000966332772540e+00, 9.993114007411373e-01, 9.975362702189898e-01, 9.956442306333592e-01, 9.936333924912825e-01, 9.908677480361242e-01, 9.882326326262749e-01, 9.853620567056602e-01, 9.822305093671991e-01, 9.788185853162172e-01, 9.751026333215268e-01, 9.710631852370086e-01, 9.666759668947944e-01, 9.619242192293307e-01, 9.567841986369235e-01, 9.512394303101863e-01, 9.452700238623795e-01, 9.388615698236068e-01, 9.319946435581106e-01, 9.246592033932568e-01, 9.168383396399868e-01, 9.085218034087421e-01, 8.996967011299613e-01, 8.903562054918268e-01, 8.804877931535187e-01, 8.700884209228057e-01, 8.591492134848259e-01, 8.476686394755906e-01, 8.356428970797861e-01, 8.230753889817990e-01, 8.099649296155544e-01, 7.963204506324437e-01, 7.821460539775005e-01, 7.674541821769616e-01, 7.522563457568547e-01, 7.365702052057368e-01, 7.204090552899627e-01, 7.037975107157410e-01, 6.867542812151157e-01, 6.693041888771051e-01, 6.514710959179395e-01, 6.332854832820911e-01, 6.147685389896460e-01, 5.959553778639692e-01, 5.768737955463938e-01, 5.575534287167304e-01, 5.380320138068979e-01, 5.183454027643563e-01, 4.985259415650634e-01, 4.786156067459849e-01, 4.586473038370941e-01, 4.386643656872842e-01, 4.187046888325280e-01, 3.988123056192917e-01, 3.790262923635886e-01, 3.593914828698096e-01, 3.399474132903109e-01, 3.207392420889753e-01, 3.018061113177048e-01, 2.831905952786929e-01, 2.649288369241889e-01, 2.470608550624402e-01, 2.296201119084317e-01, 2.126433716126151e-01, 1.961601816145380e-01, 1.802035203864437e-01, 1.647996883470626e-01, 1.499787548077656e-01, 1.357643522991611e-01, 1.221842534547464e-01, 1.092601994264172e-01, 9.701788451015501e-02, 8.547680283183663e-02, 7.465976378295235e-02, 6.458254322751883e-02, 5.526281189874138e-02, 4.670976978373095e-02, 3.893244425578719e-02, 3.192976013776996e-02, 2.569810636390756e-02, 2.022259265088492e-02, 1.548317776486452e-02, 1.144924909653903e-02, 8.076482660383199e-03, 5.300044080947794e-03, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, +0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00
  33. 33. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: + 1.489582832987000e-03 1.889770382231583e-03 2.353000800169909e-03 2.884104959764029e-03, 3.488213786635855e-03 4.170040431489613e-03 4.934298832466617e-03 5.787076505403503e-03, 6.733811743137561e-03 7.779130464154915e-03 8.927044958757816e-03 1.018202888968871e-02, 1.154910606525086e-02 1.303349217699797e-02 1.463951288465963e-02 1.637155619860352e-02, 1.823455383898077e-02 2.023309488998589e-02 2.237116158648752e-02 2.465237348403478e-02, 2.708101935270475e-02 2.966159685753317e-02 3.239884850877327e-02 3.529601774976465e-02, 3.835663329277230e-02 4.158447932459513e-02 4.498322421745353e-02 4.855610986150206e-02 5.230596475016741e-02 5.623624576084146e-02 6.035055738891727e-02 6.465186317477950e-02, 6.914195749790462e-02 7.382288203064732e-02 7.869709331995660e-02 8.376761638427657e-02, 8.903563687211118e-02 9.450199243028472e-02 1.001680193006426e-01 1.060356225286319e-01, 1.121060220821844e-01 1.183788547045326e-01 1.248534855777947e-01 1.315302847610869e-01, 1.384103079528939e-01 1.454931890869180e-01 1.527772946853750e-01 1.602608842337125e-01, 1.679435556337752e-01 1.758245615079801e-01 1.839020119821303e-01 1.921728622634411e-01, 2.006344295681524e-01 2.092853879977170e-01 2.181238261985594e-01 2.271462264407930e-01, 2.363479205237173e-01 2.457259744642953e-01 2.552771551741124e-01 2.649981094228982e-01, 2.748839432649996e-01 2.849296444030153e-01 2.951306505827265e-01 3.054824712370942e-01, 3.159799638238941e-01 3.266169794538543e-01 3.373873799614014e-01 3.482855915638277e-01, 3.593057693987583e-01 3.704415932452488e-01 3.816862385160692e-01 3.930329782788047e-01, 4.044749630814483e-01 4.160051103939122e-01 4.276159595085598e-01 4.393004362003260e-01, 4.510516333434032e-01 4.628616046119925e-01 4.747225454237193e-01 4.866266705542529e-01, 4.985664508456704e-01 5.105341492548225e-01 5.225212793188740e-01 5.345190505841265e-01, 5.465201916422433e-01 5.585172769552711e-01 5.705021536899105e-01 5.824658100332457e-01, 5.943991720381216e-01 6.062948176207270e-01 6.181452662624718e-01 6.299422016714543e-01, 6.416768736044914e-01 6.533411462740817e-01 6.649277540000037e-01 6.764292700223311e-01, 6.878367295965062e-01 6.991421467689277e-01 7.103379606632721e-01 7.214176027060971e-01, 7.323746102405828e-01 7.432008025932804e-01 7.538887973483771e-01 7.644315495717613e-01, 7.748223151443820e-01 7.850546571907628e-01 7.951223518167163e-01 8.050193862201107e-01, 8.147397447696774e-01 8.242774413707643e-01 8.336267114335371e-01 8.427819363777799e-01, 8.517386186427548e-01 8.604920874939698e-01 8.690376742017057e-01 8.773720451249032e-01, 8.854927938913381e-01 8.933935477349644e-01 9.010727088526728e-01 9.085249398881980e-01, 9.157483563218768e-01 9.227413839712016e-01 9.295017469413066e-01 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1.017564416918053e+00, 1.016391686789653e+00 1.015184918030332e+00 1.013950835315021e+00 1.012697033320358e+00, 1.011430749860716e+00 1.010158346781076e+00 1.008885191761748e+00 1.007592718305943e+00, 1.006805603478092e+00 1.005378742804807e+00 1.004049051787112e+00 1.002778356298787e+00, 1.001563778373068e+00 1.000404915291105e+00 9.993014844615166e-01 9.982531564931281e-01, 9.972595460676951e-01, 9.963202131848272e-01, 9.954346644968789e-01, 9.946023543844607e-01 9.938226881029791e-01, 9.930950268060122e-01, 9.924186919309267e-01, 9.917929657090736e-01 9.912170911359961e-01, 9.906902760441473e-01, 9.902117003786811e-01, 9.897805192546193e-01 9.893958602389157e-01, 9.890568243690241e-01, 9.887624937408933e-01, 9.885119364350415e-01 9.883042028597552e-01, 9.881383235740961e-01, 9.880133161159576e-01, 9.879281898513085e-01 9.878819413827574e-01, 9.878735508484809e-01, 9.879019873841568e-01, 9.879662130250981e-01 9.880651778500144e-01, 9.881978162133899e-01, 9.883630508181326e-01, 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  34. 34. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +3.821992968116373e-04, 5.337292962876158e-04 7.010318350640769e-04, 8910357994632938e-04, 1.107726421735994e-03, 1.354305556720234e-03 1.632968062524617e-03, 1 944392065549996e-03, 2.291251920978034e-03, 2.676357471188558e-03 3.102160324883627e-03, 3569302917352426e-03, 4.080147004222224e-03, 4.637409387087253e-03 5.243697651112320e-03, 5900394401532485e-03, 6.609908124535202e-03, 7.375089966000295e-03 8.197610411215884e-03, 9078195201482999e-03, 1.001888876231112e-02, 1.102272421949215e-02 1.209201783148431e-02, 1 322773320467288e-02, 1.443170227861997e-02, 1.570673344965518e-02 1.705481769961258e-02, 1 847711280171765e-02, 1.997546609433320e-02, 2.155255505248360e-02 2.320993080187466e-02, 2494800748775296e-02, 2.676898100961685e-02, 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  35. 35. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +3.538498803770035e-04, 4.595886345493055e-04, 5.595519647227489e-04, 6.718404887323839e-04, 7.919323614002698e-04, 9.254835101516548e-04, 1.069418485858920e-03, 1.227927169310031e-03, 1.398277791978983e-03, 1.584491535026729e-03, 1.783653266717233e-03, 1.999873692180148e-03, 2.230687004705732e-03, 2.479549413444207e-03, 2.744274680521470e-03, 3.028517203082985e-03, 3.329799454594260e-03, 3.651493788541270e-03, 3.991659081158673e-03, 4.353535478916468e-03, 4.734803493964832e-03, 5.139354888882466e-03, 5.564965156664017e-03, 6.015065135312130e-03, 6.487669532207667e-03, 6.986108359341676e-03, 7.507986430774601e-03, 8.056692238103912e-03, 8.629882322202329e-03, 9.230898632007642e-03, 9.857619542786990e-03, 1.051343406844975e-02, 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  36. 36. El aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ventanas de síntesis (290) comprende una sucesión, en orden hacia delante o hacia atrás, formada por los siguientes valores con ± 1 % de tolerancia: +3.235700349233950e-04, 3.821992968116373e-04, 4.346763076430269e-04, 4.841399974556557e-04, 5.337292962876158e-04, 5.864735900759105e-04, 6.428827504324996e-04, 7.010318350640768e-04, 7.608344672311270e-04, 8.240821499679188e-04, 8.910357994632938e-04, 9.604008359868557e-04, 1.032187650884365e-03, 1.107726421735994e-03, 1.187132578842487e-03, 1.269300730654068e-03, 1.354305556720234e-03, 1.443403284874795e-03, 1.536663296357133e-03, 1.632968062524617e-03, 1.732380147404573e-03, 1.836145247521724e-03, 1.944392065549996e-03, 2.056125836181849e-03, 2.171386021601719e-03, 2.291251920978034e-03, 2.415808383814314e-03, 2.544144440874477e-03, 2.676357471188558e-03, 2.813551797283812e-03, 2.955803613263345e-03, 3.102160324883627e-03, 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0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00.
  37. 37. Un aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ven tanas de síntesis se define de modo que presente una primera derivación numérica entre -0,01 y 0,01.
  38. 38. Un aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ven tanas de síntesis se define de modo que presente una segunda derivación numérica entre -10-4 y 10-4
  39. 39. Un aparato según cualquiera de las reivindicaciones 6 a 21, en el que la función de formación en ven tanas de síntesis se define de modo que presente una segunda derivación numérica entre -10-5 y 10-5.
  40. 40. Un procedimiento para codificar una señal de audio que comprende una pluralidad de tramas, en el que el procedimiento comprende el hecho de: efectuar un análisis de transformación de coseno modificada, MDCT, para transformar una representación en el dominio de tiempo, TD, de la señal de audio, o una versión procesada de la misma, en una representación en el dominio de la frecuencia, FD, mediante una función de formación en ventanas de análisis (40, 50, 240, 70) que presenta una parte de intersección (44, 244) que intersecta con una función lineal (40', 240') en correspondencia con al menos cuatro puntos (#1, #2, #3, #4), en el que la función de formación en ventanas de análisis se define de modo que sea asimétrica, en el que la función de formación en ventanas de análisis (40, 240) se define de modo que sea, en la parte de intersección (44, 94, 244): mayor que la función lineal (40', 240') en un primer intervalo (41,241) entre un primer punto de intersección (#1) y un segundo punto de intersección (#2); menor que la función lineal (40', 240') en un segundo intervalo (42, 242) entre el segundo punto de intersección (#2) y un tercer punto de intersección (#3); mayor que la función lineal (40', 240') en un tercer intervalo (43, 243) entre el tercer punto de intersección (#3) y un cuarto punto de intersección (#4), en el que la función de formación en ventanas de análisis se define de modo que el valor máximo absoluto (41', 241') esté en uno del primer y del tercer intervalo, caracterizado porque la función lineal (40, 240) es una función constante con valor constante 1.
  41. 41. Un procedimiento para decodificar señal de audio, o una versión procesada de la misma, definida en el dominio de la frecuencia, FD, en el que el procedimiento comprende el hecho de efectuar una síntesis de transformación de coseno modificada, MDCT, para transformar la representación en el FD de una señal de audio, o una versión procesada de la misma, en una representación en el dominio de tiempo, TD, mediante una función de formación en ventanas de síntesis (90) que presenta una parte de intersección (94) que intersecta con una función lineal en correspondencia con al menos cuatro puntos (#1, #2, #3, #4), en el que la función de formación en ventanas de síntesis (90, 290) se define de modo que sea, en la parte de intersección: mayor que la función lineal en un primer intervalo entre un primer punto de intersección y un segundo punto de intersección; menor que la función lineal en un segundo intervalo entre el segundo punto de intersección y un tercer punto de intersección; mayor que la función lineal en un tercer intervalo entre el tercer punto de intersección y un cuarto punto de intersección, en el que la función de formación en ventanas de síntesis se define de modo que el valor máximo absoluto esté en uno del primer y del tercer intervalo, caracterizado porque la función lineal es una función constante con valor constante 1.
  42. 42. Unidad de almacenamiento no transitorio que almacena instrucciones que, cuando se ejecutan en un procesador, hacen que el procesador realice un procedimiento según la reivindicación 40 o 41.
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