BR122016027554B1 - signal processing apparatus for filtering and performing high-frequency reconstruction of an audio signal - Google Patents

Abstract

OPERATABLE APPLIANCE TO DETERMINE N COEFFICIENTS OF A PROTOTYPE FILTER. The invention relates to sub-sampled, modulated digital filter banks, as well as methods and systems for designing such filter banks. In particular, the present invention relates to a method and apparatus for improving low-delay modulated digital filterbanks. The method employs modulation of an asymmetric low-pass prototype filter, and a new method to optimize the coefficients of this filter. In addition, a specific design for a 64-channel filterbank is provided using a prototype filter length of 640 coefficients and a system delay of 319 samples. The method substantially reduces artifacts due to aliasing that emerge from independent modifications of subband signals, for example when using a filter bank as a spectral equalizer. The method is preferably implemented in software that runs on a standard PC or a digital signal processor (DSP), but it can also be encoded on a client chip. The method offers enhancements to various types of digital equalizers, adaptive filters, multiband compilers, and spectral envelope adjustment filterbanks used in high-frequency reconstruction (HFR) or systems (...).

Description

[001] Divided from PI1008458-4, filed on 02.17.2010.

[002] The present invention relates to subsampled modulated digital filter banks, as well as methods and systems for the design of such filter banks. In particular, it provides a new design method and apparatus for a near-perfect reconstruction low-delay complex exponential or cosine modulated filterbank optimized for suppression of aliasing that emerges from modifications of spectral coefficients or sub-signals. band. In addition, a specific design for a 64-channel filterbank is provided using a prototype filter length of 640 coefficients and a system delay of 319 samples.

[003] The teachings in this document may be applicable to digital equalizers as outlined, for example, in "An Efficient 20 Band Digital Audio Equalizer" AJS Ferreira, JMN Viera, AES preprint, 98th Convention 1995 February 25-28 Paris, NY, USA ; adaptive filters, as outlined, for example, in "Adaptive Filtering in Subbands with Critical Sampling: Analysis, Experiments, and Application to Acoustic Echo Cancellation" A. Gilloire, M. Vetterli, IEEE Transactions on Signal Processing, vol. 40, no. 8, August, 1992; multiband compressors; and to audio coding systems using high frequency reconstruction (HFR) methods; or audio coding systems that employ so-called parametric stereo techniques. In the last two examples, a digital filter bank is used to adaptively adjust the spectral envelope of the audio signal. An HRF system taken as an example is the Spectral Band Replication (SBR) system outlined, for example, in WO 98/57436, and a parametric stereo system outlined in, for example, EP 1410687.

[004] Throughout this disclosure, including the embodiments, the expressions "subband signals" or "subband samples" indicate the output signal or output signals or output sample or output samples from the part analysis of a digital filter bank or output from a forward transform, that is, the transform that operates on the time-domain data of a transform-based system. Examples of the output of such forward transforms are the frequency domain coefficients from a digital windowed Fourier transform (DFT) or the samples output from the analysis stage of a modified discrete cosine transform (MDCT).

[005] Throughout this disclosure, including the embodiments, the term "aliasing" indicates a non-linear distortion that results from decimation and interpolation, possibly in combination with modification (e.g., attenuation or quantization) of the subband samples in an undersampled digital filter bank.

[006] A digital filter bank is a collection of two or more parallel digital filters. The analysis filter bank divides the incoming signal into a number of separate signals called subband signals or spectral coefficients. The filter bank is critically sampled or maximally decimated when the total number of subband samples per unit of time is the same as that for the input signal. A so-called synthesis filter bank combines the subband signals into an output signal. A popular type of critically sampled filterbanks is the cosine modulated filterbank where filters are obtained in cosine modulation of a low-pass filter, a so-called prototype filter. The cosine modulated filter bank offers effective implementations and is often used in natural audio encoding systems. For further details reference is made to "Introduction to Perceptual Coding" K. Brandenburg, AES, Collected Papers on Digital Audio Bitrate Reduction, 1996.

[007] A common problem in filter bank design is that any attempt to alter subband samples or spectral coefficients, for example by applying an equalization gain curve or quantizing the samples, typically forms "artifacts" of aliasing on the output signal. Therefore, filterbank designs are desirable, which reduce such artifacts even when subband samples are subjected to severe modifications.

[008] A possible approach is the use of oversampled filter banks, that is, not critically sampled. An example of an oversampled filter bank is the class of complex exponential modulated filter banks where an imaginary sine modulated part is added to the real part of a cosine modulated filter bank. Such a complex exponential modulated filterbank is described in EP 1374399 which is hereby incorporated by reference.

[009] One of the properties of complex exponential modulated filterbanks is that they are free from the main aliasing terms present in cosine modulated filterbanks. As a result, such filterbanks are typically less subject to artifacts induced by modifications to the subband samples. Nevertheless, other aliasing terms remain, and sophisticated design techniques for the prototype filter of such a complex exponential modulated filterbank should be applied to minimize mismatches such as aliasing that emerges from modifications to the subband signals. Typically, the remaining aliasing terms are less significant than the main aliasing terms.

[0010] Another property of filter banks is the amount of delay a signal incurs in passing through such filter banks. In particular for real-time applications, such as audio and video streams, the filter or system delay should be low. One possible approach to obtain a filterbank that has a low total system delay, that is, a low delay or latency of a signal that traverses an analysis filterbank followed by a synthesis filterbank is to use filters short symmetric prototypes. Typically, the use of short prototype filters leads to relatively poor frequency band separation characteristics, and large areas of frequency overlap between adjacent subbands. As a result, short prototype filters usually do not allow for a filterbank design that adequately suppresses aliasing when modifying subband samples, and other approaches to low-delay filterbank design are required.

[0011] It is, therefore, desirable to provide a design method for filter banks that combines a number of desirable properties. Such properties are a high level of non-susceptibility to signal deterioration such as aliasing subject to modification of subband signals; a low delay or latency of a signal that traverses the analysis and synthesis filterbanks; and a good approximation of the perfect rebuild property. In other words, it is desirable to provide a design method for filter banks that generate a low level of errors. Undersampled filterbanks typically generate two types of errors, linear distortion from the passband term that can be further divided into amplitude and phase errors, and nonlinear distortion that emerges from the aliasing terms. Even though a "good approximation" of the PR (perfect reconstruction) property could keep all these errors to a low level, it can be beneficial from a perceptual standpoint to place greater emphasis on reducing distortions caused by aliasing.

[0012] Furthermore, it is desirable to provide a prototype filter that can be used to design an analysis and/or synthesis filter bank that presents such properties. It is another desirable property of a filterbank to have an almost constant group delay to minimize artifacts due to phase dispersion of the output signal.

[0013] The present document shows that deteriorations arising from modifications of subband signals can be significantly reduced by employing a filter bank design method referred to as the improved aliasing term minimization (IATM) method for optimization of symmetric or asymmetric prototype filters.

[0014] The present document teaches that the concept of pseudo QMF (Quadrature Mirror Filter) designs, that is, nearly perfect reconstruction filterbank designs can be extended to cover low-delay filterbank systems employing asymmetric prototype filters. As a result, nearly perfect reconstruction filterbanks with a low system delay, low susceptibility to aliasing, and/or low level of passband errors including phase dispersion can be designed. Depending on particular needs, the emphasis placed on any of the filter bank properties can be changed. Hence, the filter bank design method according to this document alleviates the current limitations of PR filter banks used in an equalization system or other systems that modify spectral coefficients.

[0015] The design of a low-delay complex exponential modulated filter bank according to the present document can comprise the steps: - a design of an asymmetric low-pass prototype filter with a cut-off frequency of π/2M, optimized for desired aliasing and rejection of passband errors, further optimized for a system delay D, M being the number of channels in the filter bank; and - a construction of an M-channel filter bank through complex exponential modulation of the optimized prototype filter.

[0016] Furthermore, the operation of such low-delay complex exponential modulated filterbank according to the present document can comprise the steps: - a filtering of a signal in real evaluated time domain through the analysis part from the filter bank; - a modification of the complex valued subband signals, for example, in accordance with a desired, possibly time-varying, equalizer adjustment; - a filtering of the modified complex value subband samples through the synthesis part of the filterbank; and - a computation of the real part of the output signal in the time domain of the complex value obtained from the synthesis part of the filterbank.

[0017] In addition to presenting a new filter design method, the present document describes a specific design of a 64-channel filter bank that has a prototype filter length of 640 coefficients and a system delay of 319 samples.

[0018] The teachings of this document, notably the proposed filter bank and the filter banks designed according to the proposed design method, can be used in various applications. Such applications are the enhancement of various types of digital equalizers, adaptive filters, multi-band compressors and adaptive envelope adjustment filter banks used in parametric HFR or stereo systems.

[0019] According to a first aspect, a method for terminating N coefficients of an asymmetrical prototype filter p0 for use to build a low-delay under-delayed analysis/synthesis filterbank of M channels is described. The analysis/synthesis filterbank may comprise M analysis filters hk and M synthesis filters fk where k takes values from 0 to M-1, and where typically M is greater than 1. The analysis filterbank - if/synthesis has a global transfer function that is typically associated with the analysis and synthesis filter coefficients, as well as with the decimation and/or interpolation operations.

[0020] The method comprises the step of choosing a filter bank target transfer function that comprises a target delay D. Typically a target delay D that is less than or equal to N is selected. The method further comprises the step of determining a composite objective function etot comprising a passband error term et and an aliasing error term ea. The passband error term is associated with the deviation between the filter bank transfer function and the target transfer function and the aliasing error term and is associated with errors incurred due to undersampling, i.e., decimation and/ or filter bank interpolation. In another method step, the N coefficients of the asymmetric prototype filter p0 are determined that reduce the composite objective function etot.

[0021] Typically the step of determining the objective error function etot and the step of determining the N coefficients of the asymmetric prototype filter p0 are iteratively repeated until a minimum of the objective error function etot is reached. In other words, the etot goal function is determined based on a given set of prototype filter coefficients, and an updated set of prototype filter coefficients is generated by reducing the goal error function. This process is repeated until no further reductions of the objective function can be achieved by modifying the prototype filter coefficients. This means that the step of determining the etot objective error function may comprise determining a value for the etot composite objective function for given coefficients of the prototype filter p0 and the step of determining the N coefficients of the asymmetrical prototype filter p0 may comprise determining coefficients updated from the prototype filter p0 based on the gradient of the composite objective function etot associated with the coefficients from the prototype filter p0.

com P(a>)e jaD sendo a função de transferência alvo, e

onde Hk(z) e Fk(z) são as transformadas-z dos filtros de análise e síntese hk(n) e fk(n) , respectivamente.[0022] According to another aspect, the compound objective error function etot is given by etot (a) = a et + (1 - a) ea with e1 being the passband error term, ea being o aliasing error term e α being a weighting constant taken in values between 0 and 1. The passband error term e1 can be determined by accumulating the squared deviation between the filter bank transfer function and the target transfer function for a plurality of frequencies. In particular, the bandwidth error term e1 can be calculated as

with P(a>) and jaD being the target transfer function, and

where Hk(z) and Fk(z) are the z-transforms of the analysis and synthesis filters hk(n) and fk(n) , respectively.

[0023] The aliasing error term ea is determined by accumulating the square magnitude of the aliasing gain terms for a plurality of frequencies. In particular, the aliasing error term ea is calculated as

[0024] The I-th aliasing gain term evaluated in the unit circle with W= e-i2π/M, where Hk(z) and Fk (z) are the z transforms of the analysis and synthesis filters hk(n) and fk(n), respectively. The annotation Al*(z) is the z-transform of the complex conjugate sequence al(n).

com n = 0 . N-1, para os M filtros de análise do banco de filtro de análise e

com n = 0 . N-1, para os M filtros de síntese do banco de filtro de síntese.[0025] According to another aspect, the step of determining a value for the composite objective function etot may comprise generating the hk(n) analysis filters and the fk(n) synthesis filters of the analysis/synthesis filter bank based on the prototype filter p0(n) using cosine modulation, sine modulation, and/or complex exponential modulation. In particular, analysis and synthesis filters can be determined using cosine modulation as

with n = 0 . N-1, for the M analysis filters of the analysis filter bank and

with n = 0 . N-1, for the M synthesis filters from the synthesis filter bank.

com n = 0 ... N-1, e A sendo uma constante arbitrária para os M filtros de análise do banco de filtro de análise e

com n = 0 . N-1, para os M filtros de síntese do banco de filtro de síntese.[0026] The analysis and synthesis filters can also be determined using complex exponential modulation such as

with n = 0 ... N-1, and A being an arbitrary constant for the M analysis filters of the analysis filterbank and

with n = 0 . N-1, for the M synthesis filters from the synthesis filter bank.

[0027] According to another aspect, the step of determining a value for the composite objective function etot may comprise setting at least one of the filter bank channels to zero. This can be achieved by applying zero gains for at least one analysis and/or synthesis filter, ie the filter coefficients hk and/or fk can be set to zero for at least one channel k. In one example, a predetermined number of low frequency channels and/or a predetermined number of high frequency channels can be set to zero. In other words, the low frequency filter bank channels k=0 to Clow; with Clow greater than zero can be set to zero. Alternatively or in addition, high frequency filter bank channels k=Chigh to M-1 with Chigh less than M-1 can be set to zero.

[0028] In this case, the step of determining the value for the composite objective function etot may comprise generating the analysis and synthesis filters for the aliasing terms Clow and M-Clow and/or Chigh and M-Chigh using exponential modulation complex. It can further comprise generating the analysis and synthesis filters for the remaining aliasing terms using cosine modulation. In other words, the optimization procedure can be done in a complex partially evaluated way where the aliasing error terms that are free from the main aliasing are calculated using real evaluated filters, eg filters generated using cosine modulation, and where the Aliasing error terms that can load the main aliasing into an actual evaluated system are modified by complex value processing, for example, using filters modulated by complex exponentials.

[0029] According to another aspect, the analysis filter bank can generate M subband signals from an input signal using the M analysis filters hk. These M subband signals can be decimated by an M factor, producing decimated subband signals. Typically the decimated subband signals are modified, for example, for equalization purposes or for compression purposes. The possibly modified decimated subband signals can be higher rate sampled by a factor M and the synthesis filter bank can generate an output signal from the higher rate sampled decimated subband signals using the M filters of synthesis fk.

[0030] According to another aspect, an asymmetric prototype filter p0(n) comprising coefficients derivable from the coefficients in Table 1 by any of the rounding, truncation, scaling, undersampling or oversampling operations is described. Any combination of rounding, truncation, scaling, undersampling, or oversampling operations are possible.

[0031] The filter coefficients rounding operation can comprise any of the following: round to more than 20 significant digits, more than 19 significant digits, more than 18 significant digits, more than 17 significant digits, more than than 16 significant digits, more than 15 significant digits, more than 14 significant digits, more than 13 significant digits, more than 12 significant digits, more than 11 significant digits, more than 10 significant digits, more than 9 significant digits, more than 8 significant digits, more than 7 significant digits, more than 6 significant digits, more than 5 significant digits, more than 4 significant digits, more than 3 significant digits, more than 2 significant digits, more than 1 significant digit, 1 significant digit.

[0032] The filter coefficient truncation operation can comprise any of the following: truncate to more than 20 significant digits, more than 19 significant digits, more than 18 significant digits, more than 17 significant digits, more than than 16 significant digits, more than 15 significant digits, more than 14 significant digits, more than 13 significant digits, more than 12 significant digits, more than 11 significant digits, more than 10 significant digits, more than 9 significant digits, more than 8 significant digits, more than 7 significant digits, more than 6 significant digits, more than 5 significant digits, more than 4 significant digits, more than 3 significant digits, more than 2 significant digits, more than 1 significant digit, 1 significant digit.

[0033] The filter coefficient scaling operation may comprise scaling up or scaling down the filter coefficients. In particular, it may comprise scaling up and/or down by the number M of filter bank channels. Such up and/or down scaling can be used to keep the input power of an input signal to the filter bank at the output of the filter bank.

[0034] The subsampling operation may comprise subsampling by a factor less than or equal to 2, less than or equal to 3, less than or equal to 4, less than or equal to 8, less than or equal to 16, less than or equal to 32 , less than or equal to 64, less than or equal to 128, less than or equal to 256. The subsampling operation may further comprise determining the undersampled filter coefficients as the average value of adjacent filter coefficient. In particular, the average value of adjacent filter coefficients R can be determined as the undersampled filter coefficient where R is the undersampling factor.

[0035] The oversampling operation may comprise oversampling by a factor less than or equal to 2, less than or equal to 3, less than or equal to 4, less than or equal to 5, less than or equal to 6, less than or equal to 7, less than or equal to 8, less than or equal to 9, less than or equal to 10. The oversampling operation may further comprise determining the oversampled filter coefficients as the interpolation between two filter coefficients.

[0036] According to another aspect, a filterbank comprising M filters is described. The filters in this filterbank are based on the asymmetrical prototype filters described in this document and/or the asymmetrical prototype filters determined using the methods outlined in this document. In particular, the M filters can be a modulated version of the prototype filter and the modulation can be a cosine modulation, sine modulation and/or complex exponential modulation.

[0037] According to another aspect, a method for generating decimated subband signals with low aliasing sensitivity that emerges from modifications of said subband signals is described. The method comprises the steps of determining analysis filters of an analysis/synthesis filterbank according to methods outlined in this document; filtering a real-valued time domain signal through said analysis filters to obtain complex value subband signals and decimate said subband signals. Furthermore, a method for generating a real valued output signal from a plurality of subband signals of complex values with low aliasing sensitivity that emerges from modifications of said subband signals is described. The method comprises the steps of determining synthesis filters of an analysis/synthesis filterbank according to the methods outlined in this document; interpolating said plurality of complex valued subband signals, filtering said plurality of interpolated subband signals through said synthesis filters; generating a complex valued time domain output signal as the sum of the signals obtained from said filtering; and taking the real part of the complex value time domain output signal as the real value output signal.

[0038] According to another aspect, an operating system of generating subband signals from an input signal in the time domain is described, in which the system comprises an analysis filter bank that was generated in accordance with methods outlined in this document and/or which is based on the prototype filters outlined in this document.

[0039] It should be noted that aspects of the methods and systems that include their preferred embodiments, as outlined in this Patent Application, may be used alone or in combination with the other aspects of the methods and systems disclosed herein. Furthermore, all aspects of the methods and systems outlined in this patent application may be arbitrarily combined. In particular, aspects of the embodiments can be combined with one another in an arbitrary manner.

[0040] The present invention will now be described by way of illustrative examples not limiting in scope, with reference to the accompanying drawings, in which:

[0041] Figure 1 illustrates the analysis and synthesis sections of a digital filter bank; Figure 2 shows the stylized frequency responses for a set of filters, to illustrate the adverse effect of modifying the subband samples in a cosine modulated, i.e., rated real, filter bank; Figure 3 shows a flowchart of an example optimization procedure; Figure 4 shows a plot in the time domain and frequency response of a prototype filter optimized for a low-delay modulated filter bank that has 64 channels and a total system delay of 319 samples; and Figure 5 illustrates an example of the analysis and synthesis parts of a low-delay complex exponential modulated filterbank system.

[0042] It should be understood that the present teachings are applicable to a range of implementations that incorporate digital filterbanks other than those explicitly mentioned in this Patent. In particular, the present teachings can be applicable to other methods for designing a filter bank based on a prototype filter.

[0043] In what follows, the global transfer function of an analysis/synthesis filterbank is determined. In other words, the mathematical representation of a signal that traverses such a filterbank system is described. A digital filter bank is a collection of M, M being two or more parallel digital filters that share a common input or common output. For details of such filter banks reference is made to "Multirate Systems and Filter Banks" P.P. Vaidyanathan Prentice Hall: Englewood Cliffs, NJ, 1993. When sharing a common input, the filterbank can be called an analysis bank. The analysis bank divides the incoming signal into M separate signals called subband signals. Analysis filters are indicated Hk(z) where k=0, ...M-1. The filterbank is critically sampled or maximally decimated when the subband signals are decimated by a factor M. Thus, the total number of subband samples per unit of time across all subbands is the same as the number of samples per time unit for the input signal. The synthesis bank combines these subband signals into a common output signal. Synthesis filters are indicated Fk(z) for k=0, ...M-1.

[0044] A maximally decimated filterbank with M channels or subbands is shown in figure 1. The analysis part 101 produces from the input signal X(z) the subband signals Vk(z) which constitute the signals to be transmitted, stored or modified. The synthesis part 102 recombines the signals Vk(z) to the output signal AX(z).

[0045] The recombination of Vk(z) to obtain the approximation AX(z) of the original signal X(z) is subject to several potential errors. The errors can be due to an approximation of the perfect reconstruction property, and include non-linear deterioration due to aliasing, which can be caused by subband decimation and interpolation. Other errors that result from approximations of the perfect reconstruction property may be due to linear deteriorations such as phase and amplitude distortion.

onde W = e-i2π/M. As saídas dos interpoladores 105, também referidas como unidades de amostragem para cima, são fornecidas por

e a soma dos sinais obtidos a partir dos filtros de síntese 106 pode ser escrita como

é o ganho para o I-ésimo termo de aliasing X(zW l). A equação 4 mostra que XX(z) é uma soma de M componentes que consistem no produto do sinal de entrada modulado X(zWl)e o termo de ganho de aliasing correspondente A (z) . A equação 4 pode ser reescrita como

[0046] Following the annotations of figure 1, the outputs of the analysis filters Hk(z) 103 are Xk (z) = Hk (z) X (z), (1) where k=0, ...M-1 . Reducers 104 also referred to as down sampling units provide the outputs.

where W = e-i2π/M. The outputs of interpolators 105, also referred to as up sampling units, are provided by

and the sum of the signals obtained from the synthesis filters 106 can be written as

is the gain for the I-th aliasing term X(zW l). Equation 4 shows that XX(z) is a sum of M components consisting of the product of the modulated input signal X(zWl) and the corresponding aliasing gain term A(z) . Equation 4 can be rewritten as

[0047] The last sum on the right hand side (RHS) constitutes the sum of all unwanted aliasing terms.

é a função transferência global ou função distorção. A equação 8 mostra que dependendo de Hk(z) e Fk(z), T(z) poderia ser livre de ambas, da distorção de fase e da distorção de amplitude. A função transferência global deveria, neste caso, ser simplesmente um retardo de D amostras com um fator de escala constante e, isto é, T (z) = cz - D, (9) que, substituída na equação 7, fornece X(z) = cz -DX(z) . (10)[0048] Canceling all aliasing, that is, forcing this sum to zero through proper choices of Hk(z) and Fk(z), provides:

is the global transfer function or distortion function. Equation 8 shows that depending on Hk(z) and Fk(z), T(z) could be free from both phase distortion and amplitude distortion. The global transfer function should, in this case, be simply a delay of D samples with a constant scale factor e, ie, T(z) = cz - D, (9) which, substituted in equation 7, gives X(z ) = cz -DX(z) . (10)

[0049] The type of filters that satisfies equation 10 is said to have the perfect reconstruction property (PR). If equation 10 is not perfectly satisfied, although approximately satisfied, the filters are of the approximate perfect reconstruction filter class.

[0050] In what follows, a method for designing analysis and synthesis filter banks from a prototype filter is described. The resulting filter banks are referred to as cosine modulated filter banks. In the traditional theory for cosine modulated filterbanks, the hk(n) analysis filters and the fk(n) synthesis filters are cosine modulated versions of a symmetrical low-pass prototype filter p0(n), ie.

[0051] Respectively, where M is the number of channels in the filter bank and N is the order of the prototype filter.

[0052] The above cosine modulated analysis filterbank produces real evaluated subband samples for real evaluated input signals. Subband samples are down-sampled by an M factor, making the system critically sampled. Depending on the choice of the prototype filter, the filterbank can constitute an approximate perfect reconstruction system, i.e. a so-called pseudo QMF bank described, for example, in US 5,436,940, or a perfect reconstruction (PR) system. An example of a PR system is the modulated superimposed transform (MLT) described in more detail in "Lapped Transforms for Efficient Transform/Subband Coding" H.S. Malvar, IEEE Trans ASSP, vol. 38, no. 6, 1990. The global delay or system delay for a traditional cosine modulated filterbank is N.

[0053] To obtain filter bank systems that have lower system delays, this document teaches to replace the symmetrical prototype filters used in conventional filterbanks by asymmetrical prototype filters. In the prior art, the design of asymmetric prototype filters was restricted to systems having the perfect reconstruction property PR. Such a perfect reconstruction system using asymmetric prototype filters is described in EP 0874458. However, the perfect reconstruction constraint imposes limitations on a filter bank used, for example, in an equalization system due to the restricted degrees of freedom when designing the prototype filter . It should be noted that asymmetrical prototype filters have a linear phase, that is, they have a constant group delay across all frequencies. Asymmetric filters, on the other hand, typically have a non-linear phase, that is, they have a group delay that can change with frequency.

respectivamente, onde h(n) e f(n)são os filtros protóti- pos de análise e síntese de comprimentos Nh e Nf, respectivamente, e D é o retardo total do sistema de banco de filtro. Sem limitar o escopo, os bancos de filtro modulados, estudados no que segue, são sistemas onde os protótipos de análise e síntese são idênticos, isto é f0( n) = h0( n) = p 0( n), 0 < n < Nh = Nf = N (15) onde N é o comprimento do filtro protótipo p0(n).[0054] In filterbank systems that use asymmetric prototype filters, analysis and synthesis filters can be described as

respectively, where h(n) and f(n) are the prototype filters for analysis and synthesis of lengths Nh and Nf, respectively, and D is the total delay of the filter bank system. Without limiting the scope, the modulated filterbanks, studied in what follows, are systems where the analysis and synthesis prototypes are identical, that is, f0(n) = h0(n) = p 0(n), 0 < n < Nh = Nf = N (15) where N is the length of the prototype filter p0(n).

[0055] It should be noted, however, when using the filter design schemes outlined in this document, that filter banks using different prototype filters for analysis and synthesis can be determined.

[0056] An inherent property of cosine modulation is that each filter has two pass bands, one in the positive frequency band and one that corresponds to the pass band in the negative frequency band. It can be seen that the so-called main or significant aliasing terms emerge from the frequency superposition between any of the passing bands of the negative-passing band filters with frequency-modulated versions of the positive-passing bands or, reciprocally, the positive-passing filters positive pass bands with frequency modulated versions of the negative pass bands. The last terms in equations π1 1 13 and 14, that is, the terms —I k+ -1, are selected so as to provide the nullification of the main aliasing terms in cosine modulated filter banks. However, by modifying the subband samples, the nulling of main aliasing terms deteriorates, thereby resulting in a strong aliasing impact of the main aliasing terms. It is therefore desirable to remove these main aliasing terms from the subband samples all together.

utilizando a mesma notação que antes. Isto pode ser observado como adicionar uma parte imaginária ao banco de filtro avaliado real, onde a parte imaginária consiste em versões moduladas em seno do mesmo filtro protótipo. Considerando um sinal de entrada avaliado real, a saída a partir do banco de filtro pode ser interpretada como um conjunto de sinais de sub-banda onde as partes real e imaginária são transformadas de Hilbert uma da outra. As subbandas resultantes são assim os sinais analíticos da saída avaliada real obtida a partir do banco de filtro modulado por cosseno. Daí, devido à representação de valor complexo os sinais de sub-banda são superamostrados por um fator 2.[0057] The removal of the main aliasing terms can be achieved by using the so called Complex Exponential Modulated Filter Banks, which are based on an extension of the or cosine modulation for complex exponential modulation. Such an extension produces the hk(n) parsing filters as

using the same notation as before. This can be seen as adding an imaginary part to the real rated filter bank, where the imaginary part consists of sine modulated versions of the same prototype filter. Considering a real evaluated input signal, the output from the filterbank can be interpreted as a set of subband signals where the real and imaginary parts are Hilbert transformed from each other. The resulting subbands are thus the analytical signals of the actual evaluated output obtained from the cosine modulated filterbank. Hence, due to the complex value representation the subband signals are oversampled by a factor of 2.

[0058] Synthesis filters are extended in the same way for

[0059] Equations 16 and 17 imply that the output from the synthesis bank is of complex value. Using matrix notation where Ca is a matrix with the analysis filters modulated in cosine from equation 13, and Sa is a matrix with the sine modulation of the same argument, the filters from equation 16 are obtained as Ca+jSa. In these arrays k is the row index and n is the column index. Analogously, matrix Cs has synthesis filters from equation 14, and Ss is the corresponding sine-modulated version. Equation 17 can thus be written Cs+jS, where k is the column index and n is the row index. Indicating the input signal x, the output signal y is found from y = (Cs + j Ss) (Ca + j Sa) x = (CsCa - SsSa) x + j (CsSa + SsCa) x (18)

[0060] As seen from equation 18, the real part comprises two terms; the output from the cosine modulated filter bank and one output from a sine modulated filter bank. It is easily verified that if a cosine-modulated filterbank has the PR property, then its sine-modulated version, with a change of sign, constitutes a PR system as well. Thus, assuming the real part of the output, the complex exponential modulated system offers the same reconstruction precision as the corresponding cosine modulated version. In other words, by using a real value input signal, the complex exponential modulated system output signal can be determined by assuming the real part of the output signal.

[0061] The complex exponential modulated system can be extended to also handle complex valued input signals. By extending the number of channels to 2M, that is, adding the filters for negative frequencies and keeping the imaginary part of the output signal, a pseudo QMF or PR system for complex value signals is obtained.

onde A é uma constante arbitrária (possivelmente zero) e, como antes, M é número de canais, N é o comprimento do filtro protótipo, e D é o retardo do sistema. Utilizando diferentes valores de A, implementações mais eficientes dos bancos de filtro de análise e síntese, isto é, implementações com complexidade reduzida, podem ser obtidas.[0062] It should be noted that the complex exponential modulated filter bank has only one passband for each filter in the positive frequency range. Hence, it is free from the main aliasing terms. The absence of main aliasing terms makes the unaliasing constraint from the cosine (or sine) modulated filter bank obsolete in the complex exponential modulated version. Analysis and synthesis filters can thus be provided as

where A is an arbitrary constant (possibly zero) and, as before, M is the number of channels, N is the prototype filter length, and D is the system delay. Using different values of A, more efficient implementations of the analysis and synthesis filterbanks, that is, implementations with reduced complexity, can be obtained.

[0063] Before presenting a method for optimizing prototype filters, the approaches disclosed for the design of filter banks are summarized. Based on symmetrical or asymmetrical prototype filters, filterbanks can be generated, for example, by modulating the prototype filters using a cosine function or a complex exponential function. The prototype filters for the analysis and synthesis filter banks can be different or identical. When using complex exponential modulation the main aliasing terms of the filterbanks are obsolete and can be removed, thereby reducing the aliasing sensitivity to modifications of the subband signals of the resulting filterbanks. Furthermore, by using asymmetric prototype filters the overall delay of the filter bank system can be reduced. It has also been shown that by using complex exponential modulated filter banks the output signal from a real valued input signal can be determined by assuming the real part of the complex output signal from the filter bank.

[0064] In what follows, a method for optimizing prototype filters is described in detail. Depending on the needs, optimization can be directed towards increasing the degree of perfect reconstruction, that is, reducing the combination of aliasing and amplitude distortion, reducing sensitivity for aliasing, reducing system delay, reducing distortion of phase and/or amplitude distortion reduction. To optimize the prototype filter p0(n) first expressions for the aliasing gain terms are determined. In what follows, the aliasing gain terms for a complex exponential modulated filterbank are derived. However, it should be noted that the delineated aliasing gain terms are also valid for a cosine modulated (actual rated) filter bank.

[0065] Referring to equation 4, the z-transform of the real part of the input signal x(n) is

[0066] The annotation X*(z) is the z-transform of the complex conjugate sequence x(n). From equation 4 it follows that the transform of the real part of the output signal is

são os termos de ganho de aliasing utilizados na otimiza- ção. Pode ser observado da equação 24 que

[0067] Where it was used that the input signal x(n) is evaluated real, that is, X*(zW1) = X(zW ~l). Equation 22 can be written after being rearranged

are the aliasing gain terms used in the optimization. It can be seen from equation 24 that

[0068] Specifically for real rated systems

[0069] Inspecting equation 23 and resuming the transform of equation 21, it can be seen that the real part of a0(n) must be a Dirac pulse for a PR system, ie, Ã0(z) is in the form Ã0(z) )=c zD. Furthermore, the real part of aM/2(n) must be zero, that is, ÃM/2(z) must be zero, and the ali-asing gains for l # 0, M/2, must satisfy AM -l(z)=-Al*(z) , which for a real evaluated system with equation 26 in mind, means that all ai(n), l = 1...M-1 must be zero. In pseudo QMF systems, equation 28 holds true only approximately. Furthermore, the real part of a0(n) is not exactly a Dirac pulse nor is the real part of aM/2(n) exactly zero.

[0070] Before going into further details on the optimization of prototype filters, the impact of subband sample modifications on aliasing is investigated. As already mentioned above, channel gain changes in a cosine modulated filterbank, ie using the analysis/synthesis system as an equalizer, creates severe distortion due to the main aliasing terms. In theory, the main aliasing terms cancel each other out in a pair, in a paired fashion. However, this principal aliasing term nullification theory breaks down when different gains are applied to different subband channels. Hence, the aliasing in the output signal can be substantial. To show this consider a filterbank where the channel p and the highest channels are set to zero gains, ie,

[0071] The stylized frequency responses of the analysis and synthesis filters of interest are shown in figure 2. Figure 2a shows the synthesis channel filters Fp-1(z) and Fp(z) highlighted by means of the signals of reference 201 and 202, respectively. As already indicated above, the cosine modulation for each channel results in a positive frequency filter and a negative frequency filter. In other words, the positive frequency filters 201 and 202 have corresponding negative frequency filters 203 and 204, respectively.

[0072] The p-th modulation of the analysis filter Hp-1(z), ie Hp-1(zWp) indicated by the reference signals 211 to 213 is delineated in figure 2b together with the synthesis filter Fp-1(z ), indicated by reference signals 201 and 203. In this figure, the reference signal 211 indicates the modulated version of the originally positive frequency filter Hp-1(z) and the reference signal 203 indicates the modulated version of the Hp-1( z) of originally negative frequency. Due to the p-order modulation, the negative frequency filter 213 is moved to the positive frequency area and therefore superimposes itself as a positive synthesis filter 201. The shaded superposition 220 of the filters illustrates the energy of an aliasing term main.

[0073] In figure 2c the p-th modulation Hp-1(z), ie Hp-1(zWp) indicated by the reference signals 212 and 214 is shown together with the synthesis filter Fp(z), signals of reference 202 and 204. Again the negative frequency filter 214 is moved to the positive frequency area due to pth modulation. Shaded area 211 again pictorially shows the energy of a major aliasing term and should typically uncanceled result in significant aliasing. To nullify the aliasing, the term should be the reversed polarity copy of the aliasing obtained from the intersection of the filters Hp-1(zWp,) 213, and Fp-1(zWp,) 201 of figure 2b, that is, the copy of the inverted polarity of the shaded area 220. In a cosine modulated filterbank, where the gains are unshifted, these main aliasing terms will usually completely cancel each other out. However, in this example, the gain of the analysis (or synthesis) filter p is zero, so the aliasing induced by the p-1 filters will remain non-nullified in the output signal. An equally strong aliasing residue will also emerge in the negative frequency range.

[0074] When using complex exponential modulated filter banks, complex value modulation results in only positive frequency filters. Consequently, the main aliasing terms are gone, ie there is no significant overlap between the modulated analysis filters Hp(zWp,) and their corresponding synthesis filters Fp(z) and aliasing can be significantly reduced when using such filter bank systems as equalizers. The resulting aliasing is dependent only on the degree of suppression of the remaining aliasing terms.

Hence, even when using complex exponential modulated filterbanks it is crucial to design a prototype filter for maximum suppression of aliasing gain terms, although the main aliasing terms have been removed for such filterbanks. Even though the remaining aliasing terms are less significant than the main aliasing terms, they can still generate aliasing that causes artifacts to the processed signal. Therefore, the design of such a prototype filter can preferably be performed by minimizing a composite objective function. For this purpose, several optimization algorithms can be used. Examples are, for example, linear programming methods, Simplex Downhill Method or an unconstrained gradient-based method, or other non-linear optimization algorithms. In a modality taken as an example, an initial solution for the prototype filter is selected. Using the composite objective function, a direction to modify the prototype filter coefficients is determined, which gives the highest gradient of the composite objective function. Then, the filter coefficients are modified using a certain step length, and the iterative procedure is repeated until a minimum of the composite objective function is obtained. For further details on such optimization algorithms reference is made to "Numeric Recipes in C, The Art of Scientific Computing, Second Edition" WH Press, SA Teukolsky, WT Vetterling, BP Flannery, Cambridge University Press, NY, 1992, which is incorporated For reference.

onde P(ω) é uma função simétrica avaliada real que define as faixas de banda passante e de banda suprimida e D é o retardo total do sistema. Em outras palavras, P(ω) descreve a função de transferência desejada. No caso o mais genérico, tal função de transferência compreende uma magnitude que é uma função da frequência ω. Para um sistema avaliado real a equação 31 se simplifica para

[0076] For minimization of the improved aliasing term (IATM) of the prototype filter, a preferred objective function can be indicated etot (a) = aet + (1 - ®) ea , (30) where the total error etot(α) is a weighted sum of the transfer function error e1 and the aliasing error ea. The first term on the right-hand side (RHS) of equation 23 evaluated on the unit circle, ie, for z = e jw can be used to provide a measure of the error energy t of the transfer function as

where P(ω) is a real evaluated symmetric function that defines the passband and suppressed band bands and D is the total delay of the system. In other words, P(ω) describes the desired transfer function. In the most general case, such a transfer function comprises a magnitude that is a function of the frequency ω. For a real rated system, equation 31 is simplified to

[0077] The target function P(ω) and the target delay D can be selected as an input parameter for the optimization procedure. The expression P(w)e-jwD can be referred to as the target transfer function.

[0078] A measure of the total aliasing energy ea can be calculated by evaluating the sum of all the right-hand aliasing terms (RHS) of equation 23, ie, the second term of equation 23 on the unit circle as

[0079] For real rated systems and this translates to

[0080] Overall, an optimization procedure to determine a prototype filter p0(n) can be based on the minimization of the error of equation 30. The parameter α can be used to distribute the emphasis between the transfer function and the sensitivity for alia - sing of the prototype filter. While increasing the α parameter towards 1 will place more emphasis on the transfer function error et, decreasing the α parameter towards zero will place more emphasis on the aliasing error ea. Parameters P(w) and D can be used to establish a target transfer function of the prototype filter p0(n), that is, to define the behavior of the passband and the repressed band to define the total delay of the system.

[0081] According to an example, a number of the filter bank channels k can be set to zero, for example, the upper half of the filter bank channels receive zero gain. Consequently, the filterbank is triggered to generate a large amount of aliasing. This aliasing will then be minimized through the optimization process. In other words, by setting a certain number of filterbank channels to zero the aliasing will be induced to generate an aliasing error and which can be minimized during the optimization procedure. Furthermore, the computation complexity of the optimization process can be reduced by setting filterbank channels to zero.

[0082] According to an example, a prototype filter is optimized for a real value, that is, modulated by cosine, which may be more appropriate than directly optimizing the complex value version. This is because real-value processing prioritizes remote aliasing mitigation by a greater extent than complex-value processing. However, when triggering aliasing as outlined above, the main part of the aliasing induced in this case will typically originate from the terms that carry the main aliasing terms. Hence, the optimization algorithm can spend resources on maximizing the main aliasing that is inherently not present in the resulting complex exponential modulated system. To alleviate this, optimization can be done on a partially complex system; for aliasing terms that are free from main aliasing, optimization can be done using real rated filter processing. On the other hand, aliasing terms that should carry the main aliasing terms, in a real value system, should be modified for complex value filter processing. Through such partially complex optimization, the benefits of performing the processing using real-value processing can be obtained, while still optimizing the prototype filter for use in a complex modulated filterbank system.

[0083] In an optimization taken as an example, where exactly the top half of the filter bank channels is set to zero, the only aliasing term calculated from complex value filters is the I=M/2 term of the equation 33. In this example, the function P(w) of equation 31 can be chosen as a constant of unit magnitude that ranges from - π/2 +ε to π/2 -ε where ε is a fraction of π/2 to cover the frequency range that constitutes the passband. Outside the passband function P(w) can be set to be zero or left undefined. In the latter case, the error energy of the transfer function (equation 31) is only evaluated between - π/2 +ε and π/2 -ε. Alternatively and preferred, the passband error et could be calculated over all channels k=0,...M-1 from - π to + π with P(w) being constant while aliasing is still calculated with a plurality of channels set to zero as described above.

onde a Hk(ejw) e Fk(ejw) são as transformadas DFT dos fil- tros de análise e síntese hk(n) e fk(n) como gerados dos coeficientes de filtros protótipos nesta etapa de interação a partir das equações 13 até 15, respectivamente. 2. Para obter o erro de aliasing ea para termos de aliasing não submetidos a aliasing significativa, avaliar

e Hk(e™j) e Fk(e™j) são as transformadas, isto é, as trans- formadas-z avaliadas no círculo unitário dos filtros de análise e síntese hk(n) e fk(n) a partir das equações 13 até 15. 3. Para os termos submetidos s aliasing significativa avaliar:

onde Ãl(e™j) é fornecida pela equação 24, com Al(e™j) co mo equação 37, com Hk(eWJ) e Fk(eWJ) sendo as transformadas DFT de hk(n) e fk(n) a partir das equações 19 e 20. 4. O erro é em seguida ponderado com α como

[0084] Typically, the optimization procedure is an iterative procedure where given the prototype filter coefficients p0(n)(n=0, ...N-1) at a certain interaction step, the target delay D, o number of channels M, the numbers of lowband channels set to zero IoCut, the number of highband channels set to zero hiCut and the weighting factor α, a value for the objective function for this reiteration step is calculated. Using semi-complex operations and this comprises the steps: 1. To obtain the passband error and evaluate equation 32 with P(w) being a constant use

where Hk(ejw) and Fk(ejw) are the DFT transforms of the analysis and synthesis filters hk(n) and fk(n) as generated from the prototype filter coefficients in this interaction step from equations 13 to 15 , respectively. 2. To get the aliasing error and for aliased terms not significantly aliased, evaluate

and Hk(e™j) and Fk(e™j) are the transforms, that is, the z-transforms evaluated in the unit circle of the analysis and synthesis filters hk(n) and fk(n) from the equations 13 to 15. 3. For terms submitted to significant aliasing, evaluate:

where Ãl(e™j) is given by equation 24, with Al(e™j) as equation 37, with Hk(eWJ) and Fk(eWJ) being the DFT transforms of hk(n) and fk(n) a from equations 19 and 20. 4. The error is then weighted with α as

[0085] Using any of the nonlinear optimization algorithms mentioned above, this total error is reduced by modifying the prototype filter coefficients until an optimal set of coefficients is obtained. By way of example, the direction of the maximum gradient of the error function ewt is determined for the prototype filter coefficients in a given iteration step. Using a certain step dimension, the prototype filter coefficients are modified in the direction of the maximum gradient. Modified prototype filter coefficients are used as a starting point for the subsequent iteration step. The procedure is repeated until the optimization procedure has converged to a minimum value of the etot error function.

[0086] A modality taken as an example of the optimization procedure is illustrated in Figure 3, as a flowchart 300. In a step of determining parameter 301 the parameters of the optimization procedure, that is, notably the target transfer function that comprises the target delay D, the number of channels M of the target filter bank, the number N of coefficients of the prototype filter, the weighting parameter α of the objective error function, as well as the parameters for aliasing generation, i.e. loCut and/or hiCut are defined. In an initialization step 302 a first set of prototype filter coefficients is selected.

[0087] In the passband error determination unit 303 the passband error term et is determined using the given set of coefficients of the prototype filter. This can be done using equation 32 in combination with equations 35 and 13 to 15. In the evaluated aliasing error determination unit 304 a first part eaReal of the aliasing error term ea can be determined using equations 36 and 37 in combination with equations 13 to 15. In addition, in the complex value aliasing error determination unit 305 a second part

[0088] eaCplx of the aliasing error term ea can be determined using equation 38 in combination with equations 19 and 20. As a consequence, the objective function ewt can be determined from the results of the 303 units. 304 and 305, using equation 39.

[0089] The nonlinear optimization unit 306 uses optimization methods, such as linear programming, to reduce the value of the objective function. By way of example, this can be done by determining a possibly maximum gradient of the objective function with respect to modifications of the prototype filter coefficients. In other words, these modifications of the prototype filter coefficients can be determined, which results in a possibly maximum reduction of the objective function.

[0090] If the gradient determined in unit 306 remains within predetermined limits, decision unit 307 decides that a minimum of the objective function has been reached and ends the optimization procedure in step 308. If, on the other hand, the gradient exceeds the predetermined value, so the prototype filter coefficients are updated in update unit 309. The updating of the coefficients can be performed by modifying the coefficients with a predetermined step to the direction given by the gradient. Eventually the updated coefficients from the prototype filter are re-entered as an input to the passband error determination unit 303 for another iteration of the optimization procedure.

[0091] Overall, it can be described that using the above error function and an appropriate optimization algorithm, prototype filters can be determined, which are used in relation to their degree of perfect reconstruction, that is, with respect to an aliasing low in combination with low phase and/or amplitude distortion, its resilience to aliasing due to subband modifications, its system delay and/or its transfer function. The design method provides parameters, notably a weighting parameter α, a target delay D, a target transfer function P(w), a filter length N, a number of filter bank channels M, as well as trigger parameters aliasing hiCut, loCut, which can be selected to get an optimal combination of the filter properties mentioned above. Furthermore, zero adjustment of a number of subband channels as well as partial complex processing can be used to reduce the overall complexity of the optimization procedure. As a result, asymmetrical prototype filters with an almost perfect reconstruction property, low aliasing sensitivity and a low system delay can be determined for use in a complex exponential modulated filterbank. It should be noted that the above determination scheme of a prototype filter was delineated in the context of a complex exponential modulated filterbank. If other filter bank design methods are used, for example cosine modulated or sine modulated filter bank design methods, then the optimization procedure can be adapted to generate the hk(n) analysis and synthesis filters and fk(n) using the design equations of the respective filter bank design method. By way of example, equations 13 to 15 can be used in the context of a cosine modulated filterbank.

[0092] In the following, a detailed example of a 64 channel low delay filter bank is described. Using the aforementioned proposed optimization method, a detailed example of a low-delay 64-channel (M=64) filterbank used in terms of aliasing gain will be outlined. In this example the partially complex optimization method was used and the top 40 channels were set to zero during optimization of the prototype filter, ie, hiCut =40, while the loCut parameter remained unused. Hence, all aliasing gain terms except Ãl, where l = 24, 40 are calculated using real evaluated filters. The total delay of the chosen system as D=319 and the length of the prototype filter N=640. A time-domain plot of the resulting prototype filter is provided in figure 4a and the frequency response of the prototype filter is outlined in figure 4b. The filter bank offers a passband reconstruction error (amplitude and phase) of -72 dB. The phase shift of a linear phase is less than ±0.02°, and aliasing suppression is 76 dB when no modification is made to subband samples. The actual filter coefficients are tabulated in Table 1. Note that the coefficients are scaled by a factor M=64 with respect to other equations in this document that are dependent on an absolute scaling of the prototype filter.

[0093] Although the above description of the filter bank design is based on a standard filter bank notation, an example to operate the indicated filter bank may operate in other filter bank descriptions or notations, for example, implement. -filter bank settings that allow for more efficient operation in a digital signal processor.

- xI(n) é em seguida multiplicado com uma matriz de modu-lação como

onde vk(n), k=0 63, constituem os sinais de sub-banda. O índice tempo n é em seguida fornecido em amostras de subbanda. - os sinais de sub-banda de valor complexo podem então ser modificados, por exemplo, de acordo com alguma curva de equalização gk(n) desejada, possivelmente variável com o tempo e de valor complexo como vk(m)(n) = gk(n)vk(n), 0<k<64. (43)[0094] In an example, the steps to filter a signal in time domain using the optimized prototype filter can be described as follows: - to operate the filter bank in an efficient way, the prototype filter, ie, p0 (n) from Table 1, is first arranged in the polyphase representation where each other of the polyphase filter coefficients is negated and all coefficients are time shifted as p0(639 -128m -n) = (-1)mp0 (128m + n), 0 < n < 128.0 < m < 5 (40) - the analysis stage starts with the polyphase representation of the filter being applied to the signal in the x(n) time domain to produce a vector xI(n) of length 128 as

- xI(n) is then multiplied with a modulation matrix like

where vk(n), k=0 63, constitute the subband signals. The index time n is then given in subband samples. - the complex valued subband signals can then be modified, for example, according to some desired gk(n) equalization curve, possibly time-varying and complex valued like vk(m)(n) = gk (n)vk(n), 0<k<64. (43)

[0095] The synthesis stage starts with a demodulation step of the modified subband signals as

[0096] It should be noted that the modulation steps of equations 42 and 44 can be performed in a very computationally efficient way and with fast algorithms that use Fast Fourier Transform (FFT) cores.

onde x(n) é ajustado para zero para todos os n no momento de partida.[0097] The demodulated samples are filtered with the polyphase representation of the prototype filter and accumulated to the output time domain signal i(n) according to

where x(n) is set to zero for all n at start time.

[0098] It should be noted that both floating-point and fixed-point implementations should change the numerical precision of the coefficients given in Table one to something more suitable for processing. Without limiting scope, values can be quantized to lower numerical precision by rounding, truncating and/or scaling the coefficients to integers or other representations, in particular representations that are adapted to the available resources of a hardware platform and /or software the filterbank should operate on.

[0099] Furthermore, the example above delineates operation where the output signal in the time domain is of the same sampling frequency as the input signal. Other implementations can resample the signal in time domain using different sizes, that is, different number of channels of the analysis and synthesis filter banks, respectively. However, the filter banks should be based on the same prototype filter and are obtained by resampling the original prototype filter through decimation or interpolation. As an example, a prototype filter for a 32-channel filterbank is achieved by resampling the p0(n) coefficients as

[00100] The length of the new prototype filter is then 320, and the delay is D = |_319/2_| = 159, where the operator |_-_| returns to the entire part of your argument. Table 1 - Coefficients of a 64-channel low-delay prototype filter

[00101] In what follows, different aspects of practical implementations are outlined. Using a standard real-time PC or DSP operation of a low-delay complex exponential-modulated filter bank is possible. The filter bank can also be encoded on a client chip. Figure 5a shows the structure for an effective implementation of the analysis part of a complex exponential modulated filterbank system. The analog input signal is first fed to a 501 A/D converter. The time-domain digital signal is fed to a shift register which holds 2M samples by shifting M samples at a time 502. The signals from of the shift register are then filtered through the polyphase coefficients of the prototype filter 503. The filtered signals are then combined 504 and in parallel transformed with a DCT-IV 505 and a DST-IV 506. The outputs of the cosine transforms and sine constitute the real and imaginary parts of the subband samples, respectively. The sub-band sample gains are modified according to the current spectral envelope adjuster 507 setting.

[00102] An effective implementation of the synthesis part of a low-delay complex exponential modulated system is shown in figure 5b. The subband samples are first multiplied with complex value manipulated factors, ie, channel dependent constants of complex values 511 and the real part is modulated with a DCT-IV 512 and the imaginary part with a transform. DST-IV 513. The outputs of the transforms are combined 514 and fed through the polyphase components of the prototype filter 515. The time domain output signal is obtained from the shift register 516. Finally, the digital output signal is converted back to a 517 analog waveform.

[00103] Although the implementations outlined above use DCT and DST type IV transforms, implementations using DCT type II and type III cores are equally possible (and also implementations based on DST type II and III). However, the most computationally efficient implementations for complex exponential modulated banks use pure FFT cores. Implementations that use a direct matrix-vector multiplication are also possible, but they are inferior in efficiency.

[00104] In summary, this document describes a design method for prototype filters used in analysis and synthesis filter banks. Desired properties of the prototype filters and the resulting analysis/synthesis filterbanks are near perfect reconstruction, low delay, low aliasing sensitivity, and minimal amplitude/phase distortion. An error function is proposed, which can be used in an optimization algorithm to determine appropriate coefficients of the prototype filters. The error function comprises a set of parameters that can be tuned to modify the emphasis between the desired filter properties. Preferably, asymmetrical prototype filters are used. In addition, a prototype filter is described, which provides a good compromise of desired filter properties, ie, near-perfect reconstruction, low delay, high aliasing resiliency, and minimal phase/amplitude distortion.

[00105] Although specific modalities and applications have been described herein, it will be evident to those of ordinary skill in the art that various variations in the modalities and applications described herein are possible without departing from the scope of the invention described and claimed herein. It should be understood that while certain forms of the invention have been shown and described, the invention is not limited to the specific embodiments described and shown, or to the specific methods described.

[00106] The filter design method and system, as well as the filter bank described in this document, can be implemented as software, firmware and/or hardware. Certain components can, for example, be implemented as software that operates on a digital signal processor or microprocessor. Other components can be, for example, implemented as application-specific hardware and/or integrated circuits. The signals found in the described methods and systems can be stored on media such as random access memory or optical storage media. They can be transferred over networks such as radio networks, satellite networks, wireless networks or wired networks, for example the Internet. Typical devices that make use of the filter banks described in this document are synchronization boxes or other customer premises equipment, which decode audio signals. On the coding side, filter banks can be used in broadcast stations, for example, in video audio broadcast systems.

Claims (9)

1. Signal processing apparatus for filtering and performing high-frequency reconstruction of an audio signal, the signal processing apparatus characterized in that it comprises: an analysis filter bank that receives input audio samples in the real-valued time domain and generates subband samples with complex values; a phase shifter that shifts a phase of the complex valued subband samples by an amount; a high frequency reconstructor or parametric stereo synthesizer that generates complex value modified subband samples; a phase shifter that shifts a phase of the quantity-modified complex value subband samples; and a synthesis filterbank that receives the modified subband samples with complex value and generates output audio samples in the time domain, where the analysis filterbank comprises analysis filters (hk(n) ) and the synthesis filterbank comprises synthesis filters (fk(n)) which are complex exponential modulated versions of a prototype filter (p0(n)) according to:

where M is a number of channels, A is an arbitrary constant, the prototype filter (p0(n)) has a length N, and the analysis filterbank and synthesis filterbank have a system delay. D samples theme, in which the signal processing apparatus is implemented, at least in part, by one or more hardware elements. 2. Apparatus according to claim 1, characterized in that the prototype filter p0(n) is a symmetric low-pass prototype filter or an asymmetric low-pass prototype filter. 3. Apparatus according to claim 1, characterized in that the analysis filter bank is a pseudo QMF bank. 4. Apparatus according to claim 1, characterized in that an order of the prototype filter p0(n) is equal to the delay of system D. 5. Apparatus according to claim 1, characterized in that the high frequency reconstructor performs Spectral Band Replication (SBR). 6. Apparatus according to claim 1, characterized in that a quantity value is chosen to reduce a complexity of an implementation of the apparatus. 7. Apparatus according to claim 1, characterized in that the one or more hardware elements comprise a digital signal processor, a microprocessor or a memory. 8. Apparatus according to claim 1, characterized in that a number of channels in the analysis filterbank is different from a number of channels in the synthesis filterbank. 9. Apparatus according to claim 8, characterized in that the number of channels in the analysis filterbank is 32 and the number of channels in the synthesis filterbank is 64.

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