WO2009092837A1

WO2009092837A1 - Method and apparatus for digital filtering of signals

Info

Publication number: WO2009092837A1
Application number: PCT/ES2009/000027
Authority: WO
Inventors: José Javier LOPEZ MONFORT; German Ramos Peinado
Original assignee: Universidad Politecnica De Valencia
Priority date: 2008-01-23
Filing date: 2009-01-21
Publication date: 2009-07-30
Also published as: ES2341200B2; WO2009092837A4; ES2341200A1

Abstract

Method and apparatus for digital filtering of signals that combines linear digital filters with warped linear filters.

Description

PROCEDURE AND APPLIANCE FOR DIGITAL FILTERING OF

SIGNS

D E S C R I P C I Ó N

OBJECT OF THE INVENTION

The main object of the present invention is a method and an apparatus for digital signal filtering that combines linear digital filters with deformed linear filters (warped in English terminology).

BACKGROUND OF THE INVENTION

Digital signal filtering is widely used in different fields, such as audio, video, communications, radar, seismology, etc. In this document, we will call a filter “equalization” whose objective is to improve or compensate for the non-ideal response of a system by filtering its complex response with the filter designed so that the filtered response resembles an objective response. On the contrary, when what is desired is to isolate a specific part (for example, a frequency band) of a signal to obtain certain characteristics of said signal, we will say that it is an "analysis".

On the other hand, in this document we will call "system" the device whose response you want to filter. Examples of systems may be a speaker, a radar, communications channel, etc. The following equation relates

The ideal transfer function of the filter to be designed with the objective transfer function and the system transfer function:

H _objet¡w Uω)

H _βllro (jω) = When the transfer function of the system is not of a minimum phase, its inverse will be unstable, so that the transfer function of the filtered system may only approximate the objective transfer function.

In recent years, various methods have been developed for the design of digital filters. However, when the frequency band to be equalized or analyzed covers a wide range of octaves (for example, three or higher), all these methods require a high computational cost in order to achieve a spectral resolution in the appropriate equalization throughout the range. of frequencies

Linear digital filters achieve an excellent resolution at high frequencies, but deficient at low frequencies (with respect to the sampling frequency f _s used) if high-order filters are not used, which puts a huge computational cost when the filter is implemented linear in the time domain. The computational cost is lower if it is implemented in the frequency domain by means of a Fourier transform (FFT). However, this solution introduces a latency, due to the buffering processes at the input and output, which can limit its use in real-time applications that require low latency. In audio applications, for example, this latency can be uncomfortable for listeners and musicians.

Warped or warped filters, on the other hand, allow to achieve a non-linear resolution that, depending on the choice of a parameter, can be higher at low frequencies at the cost of losing it at high frequencies. However, one of the major drawbacks of warped or warped filters is the increase in computational cost.

Therefore, there is a need for a digital filter that has a good resolution at both high and low frequencies, and that does not involve excessive computational cost or introduce unauthorized latencies. DESCRIPTION OF THE INVENTION

According to a second classification, digital filters can be divided into FIR digital filters (Finite Impulse Response) and NR digital filters (Infinite Impulse Response).

FIR digital filters are easy to design and implement, they are always stable and can correct the response in magnitude and phase at the same time. Its design can be carried out in the frequency domain or in the time domain. In the frequency domain, the simplest filter design procedure is the inversion of the Fourier transform of the desired filter response. On the other hand, in the frequency domain, the least squares approach can be used (JN Mourjopoulos, "Digital Equalization of Room Acoustics", J. Audio Eng. Soc. VoI. 42, no. 11, pp. 884-900 , Nov. 1994). The resolution of the linear filters is usually quite good at high frequencies (it depends mainly on the relationship between the sampling frequency and the order of the filter), while at low frequencies the resolution is usually too low, which results in a curl in the response of the filter at low frequencies that may be unacceptable, and that is attenuated as the order of the filter increases.

The equation that defines the transfer function of a linear FIR digital filter is the following:

H _{uιmR íz} ) = ¿^ b, (z- ^í ),

where N is the order of the filter.

On the other hand, a warped or warped FIR digital filter is obtained when the unitary delay elements z ^"1 of a linear FIR digital filter are replaced by first-order step-all filters. Therefore, the transfer function of a filter FIR digital deformation is the following: z ^" '-Λ

^H WΠR O) = ∑, _{= 0} ^b , 1 - λ - z ^"1

where N is the order of the filter and λ a parameter on which it depends that the deformation improves the resolution for high frequencies (λ> 0) or for low frequencies (λ <0).

With this type of filters a resolution in non-uniform frequency is obtained, which can be higher at high or low frequencies depending on the sign of the parameter λ.

In the case of NR digital filters, the equation that defines its transfer function is characterized by having both poles and zeros:

H UR W-A + b, - z + b -2 + ... + b - (N-I)

NEITHER

O ₀ + a _x - z --1 + a ₂ - z ^{~ 2} + ... + a _M _ _λ . _z - ^{(M ~ λ)}

On the other hand, to obtain the transfer function of a deformed NR digital filter, the unit delay elements z ^'1 are replaced by first-order step-filters and the coefficients a, by the new coefficients σ ,:

σ, = ∑ _fl , - (- A) '- * -∑α,. (- λy ι- * k ⁺ + ² 2 \ = k ι = k- \

Therefore, and in accordance with one aspect of the present invention, a digital filtering method is provided, which comprises applying a linear filtering combined with at least one deformed filtering to obtain an objective response to the response signal of a system, which is chosen based on each application.

To do this, the response signal of the system is first obtained. By For example, for the equalization of a loudspeaker, the response of the loudspeaker could be calculated using techniques such as MLS (Maximum Length Sequence), logarithmic sinusoidal scanning or periodic noise. However, it is also possible to assume, based on experience, that the response signal of the system to be equalized has certain characteristics. For example, to provide different speakers with equalizations depending on the type of music played, the response signal of the speakers is not normally calculated, but rather a series of characteristics common to all speakers are assumed. Still another possibility is to apply the digital filtering procedure to a transmitted signal, without knowing or having access to the system that originated the signal. Therefore, in this area the term "the response signal of a system" refers to all these possibilities.

Next, the objective response is chosen depending on the application. For example, to equalize speakers specifically for jazz music, the objective response is chosen from the knowledge of the type of sounds that make up that type of music. In another example related to a communications channel, the objective response of the channel would be chosen taking into account the maximum distortion that that channel can support without loss of information.

The procedure, in addition to producing significant computational savings with respect to known filtering procedures, is effective at both low and high frequencies, but to obtain optimal results it should be applied to signals that span a range of octaves around three or higher. On the other hand, it is evident to one skilled in the art that a combination, in cascade or in parallel, of linear digital filters can be simplified in a single linear digital filter. For this reason, the term "a linear filter" or "a linear filter" used herein also encompasses combinations of linear filters.

In other preferred embodiments of the invention, the operation of performing a linear filtering combined with at least one deformed filtering comprises a of the following options:

- the cascade combination of a linear filtrate and at least one deformed filtrate

- The parallel combination of a linear filtrate and at least one deformed filtrate.

A preferred application of the invention is directed to the filtering of acoustic systems, being understood as any device intended for sound reproduction, both in the final stage of reproduction and in any intermediate stage of treatment or amplification of the signal. Preferred embodiments of the procedure aimed at acoustic systems would be the cases of their application to loudspeakers or hearing aids.

According to another aspect of the invention, this also extends to computer programs, in particular computer programs contained in a carrier, adapted to carry out the operations of the described procedure. The program can be in the form of a source code, object code or an intermediate code between the source code and the object code, as a partially compiled form, or in any other suitable way to implement the operations of the invention.

The carrier can be any device or entity capable of transporting the program. For example, the carrier can comprise a storage medium, such as a ROM, a CD ROM or any other magnetic storage medium, for example a floppy disk or a hard disk. In addition, the carrier can be a transmission carrier, such as an electrical or optical signal that can be communicated through electric, optical, radio or any other way.

On the other hand, according to another aspect of the present invention, An apparatus for digital signal filtering is described, characterized in that it comprises:

- An input medium, which transmits an input signal to a processing medium. The input means, according to a preferred embodiment of the invention, comprises a digital analog conversion means and / or a digital frame receiver (when the input data is already digitized previously). The function of the digital frame receiver is to modify or adapt the format of the input signal to the processing medium.

- A processing medium, which receives the input signal from the input medium and performs a digital filtering that combines a linear filtering with at least one deformed filtering. The processing medium can be of any type capable of carrying out the digital filtering process that combines a linear digital filtering with at least one deformed digital filtering, in accordance with the previously described herein, although according to preferred embodiments , it can be a DSP, an FPGA, an ASIC, a microprocessor or a microcontroller. In addition, in the case of applications in signal analysis, the processing medium is capable of performing the calculations required to extract the information from the analysis, such as calculating characteristics such as average, effective values, graphing, etc.

In case of applying the apparatus for the digital filtering of signals of the present invention for the equalization of signals, and in accordance with a preferred embodiment of the invention, said apparatus further comprises an output means, which transmits the filtered signal from the medium. from processing to another device. In other preferred embodiments of the invention, the output means comprises a digital-analog conversion means and / or a transmitter of the data in digital format to the outside.

In accordance with preferred embodiments of the invention, the apparatus for digital signal filtering further comprises a communication medium. He communications medium can be any means that allows the device to be connected to a computer or any other external system to transfer configuration parameters of the filtrate to be implemented, results or graphs calculated by the processing means or any other type of information.

In accordance with a further preferred embodiment of the invention, the apparatus for digital signal filtering comprises a means of interface with the users, which allows them to modify parameters of the filtering. Another function of the interface means may be the visualization of results or graphs calculated by the processing means. The interface medium could be, for example, a touch screen or a keypad.

In accordance with another preferred embodiment of the invention, the apparatus for digital signal filtering also comprises a storage medium, where data relating to equalized signals or filtering parameters are stored. The storage medium could be any of those known in the art, such as a hard disk, a CD ₁ a DVD, etc.

Finally, in accordance with a further preferred embodiment of the present invention, the apparatus for digital signal filtering comprises a microcontroller, which controls the operation of the interface and communications means.

DESCRIPTION OF THE DRAWINGS

To complement the description that is being made and in order to help a better understanding of the characteristics of the invention, according to a preferred example of practical implementation thereof, a set of drawings is attached as an integral part of said description. where, for the purposes of illustration and not limitation, the following has been represented:

Figure 1.- Graph showing the equalization of a speaker with FIR filters Linear orders 100, 250, 500 and 1000 (scaled from ten to ten decibels).

Figure 2.- Graph showing the answers of the error (scaling of ten in ten decibels) and the value of e _{] og} _ _dB of linear FIR filters.

Figure 3.- Graph showing the structures of the deformed FIR filters.

Figure 4.- Graph showing an optimized structure of deformed FIR filters.

Figure 5.- Graph showing the effect of deformation as a function of parameter λ, with a sampling frequency of 48 Hz.

Figure 6.- Graph showing the resolution in deformed versus linear frequencies, with a sampling frequency of 48 Hz.

Figure 7.- Graph showing the equalization with distorted FIR filters of order one third smaller than the respective linear FIR filters, with λ = 0.766 and f _s = 48 kHz.

Figure 8.- Graph showing the error responses and the value _{iog_} _dB for the distorted FIR filters.

Figures 9 and 10.- Represent possible structures of the filter according to the present invention: in cascade and in parallel.

Figures 11 and 12.- Graphs showing the resolution curves of the filters in octaves and in Q value.

Figure 13.- Graph showing the response to equalization with filters

Deformed FIR of order 33 for two values of λ. Figure 14.- Graph showing the response of the error related to the filters of the previous graph.

Figure 15.- Graph showing the values of λ for the maximum resolution of Q as a function of the frequency for different sampling frequencies.

Figure 16.- Graph showing the equalization obtained with the proposed filter structure for N _M A _C = 250 and 100.

Figure 17. Graph showing the responses and the error values ^and _{\ og} - _dB obtained with the structure of the filter according to the present invention for NMA _C = 250 and 100.

Figure 18.- Graph showing the equalization of speaker 2 with N _MA C = 250.

Figure 19.- Comparative graph that shows the equalization obtained with the same computational cost.

Figure 20.- Graph showing a comparison between error responses and values and _Xog _ _dB .

PREFERRED EMBODIMENT OF THE INVENTION

As explained earlier in this document, an example is now shown in which the procedure of the present invention is applied to the equalization of loudspeakers, using a combination of linear and deformed digital FIR filters, demonstrating that the combination of both offers some Optimum results for the equalization of audio signals, using a low computational cost without introducing latency in the operation. These results are presented here by way of example only, and in no case are they intended to limit the scope of the present invention, which extends to combinations of linear and deformed digital filters, not necessarily FIR type. Specifically, in this example a loudspeaker of the RAMSA brand (Panasonic) has been used, which has an 8-inch bass speaker in bass-reflex configuration, and a 3/4 inch tweeter for the treble.

Linear FIR digital filters

First, the behavior of linear FIR digital filters is shown. Figure 1 shows the results of the equalization of a passive speaker with an 8-inch woofer for low frequencies and a ³ -inch tweeter for high frequencies. The linear FIR filters of this example have been designed using the least squares method in the time domain (JN Mourjopoulos, "Digital Equalization of Room Acoustics", J. Audio Eng. Soc. VoI. 42, no. 11, pp 884-900, Nov. 1994). The upper graph, centered at 0 decibels (dB) shows the unfiltered speaker response H _allav02 (ω) and the objective response H _ohjeUm {ω) is shown by a thin line. In this case, a lens consisting of a fourth order high-pass Butterworth filter at 55 Hz and a second order low-pass Butterworth filter at 18 kHz has been selected. The objective response respects the natural pass-band response of the speaker, extending its response at low frequencies in a reasonable manner without introducing an excessive gain in the filter response. The response to filters of order 100, 250, 500 and 1000, located at intervals of 10 dB are shown to avoid overlapping each other. It is observed that the equalization at high frequencies is excellent for any order, but deficient at low frequencies, although it improves with the order of the filter.

The low resolution observed in the logarithmic frequency axis at low frequencies of the linear FIR filters is due to the linear treatment of the frequency axis in the design and implementation of the filter, either in the time or frequency domain. The frequency resolution of an FIR filter is defined approximately as follows: A Vfm - ^~ - _N (1)

where Af _{F! R} is the resolution in frequency; f _s is the sampling frequency; and N is the order of the filter.

With a sampling frequency of 48 kHz, for an order of 100 a resolution of 480 Hz is obtained, for 250, 192 Hz is obtained, for 500, 96 Hz is obtained, and for 1000, 48 Hz is obtained. These resolutions are sufficient for Ia Equalization of loudspeakers at high frequencies, but not for low frequencies where resolutions of up to 5 Hz or even lower are required in the equalization and subwoofer placement. It would be necessary to design linear FIR filters of orders greater than 10,000 to achieve this resolution, with the immense computational cost that this requires if they are implemented in the time domain. To reduce the computational cost, it is possible to perform the filtering in the frequency domain by means of FFT, but at the expense of increasing the latency to extremes not admissible in applications in which delays of more than 10 milliseconds are annoying for musicians or speakers ( SE Olive, FE Toóle, "The detection of reflections in typical rooms", J. Audio Eng. Soc. 37 (7/8), 1989, 539-553).

From a subjective and psycho-acoustic point of view, linear treatment of the frequency axis of linear FIR filters is not a good choice, because the human ear behaves logarithmically, both on the frequency axis and on the frequency axis. axis of magnitudes. Subjectively speaking, the spectral distance (difference between the objective response and the filtered response of the speaker) between 1 kHz and 2 kHz has a meaning similar to one between 10 kHz and 20 kHz. Taking into account this behavior, psycho-acoustic scales such as Ia Bark and ERB have been developed (M. Karjalainen, E. Piirilá, A. Járvinen and J. Huopaniemi. "Comparison of loudspeaker equalization methods based on DSP techniques", J. Audio Eng. Soc. 47 (1/2), 1999, 14-31), and for frequencies by above 500 Hz its behavior is more similar to a logarithmic curve than to a linear curve. To measure the psycho-acoustically spectral distance and subjectively evaluate the quality of the equalization, an estimator ^e ι _og - _dB has been defined (G-Ramos, JJ López, "Filter design method for loudspeaker equalization base don NR parametric filtres", J Audio Eng. Soc. 54 (12), 2006, 1162-1178). The frequency axis is logarithmically discretized to form the ω _log vector

(Equation 2), which has a resolution of 1/48 octave, obtaining 576 frequencies between 5 Hz and 20 kHz, which is sufficient for equalization.

ω, _og = [(O ₀ G) ₁ (O ₂ (O ₃ ... ω _N _ _λ ] (2)

The error vector (equation 3) represents the difference between the objective response and the filtered loudspeaker response, all the quantities being evaluated in dB

^e V ^ω iog) [ _dB ] ⁼ H target V ^ω iog) [ _dB ] ^~ H speaker l ^ω iog) [ _dB ] ~ Hf liter V ⁰⁹ IOg) [ _dB ] W /

The expression that defines the estimator e _{] os} _ _{dB is shown below}

(Equation 4), which represents the average absolute error in dB between the objective response and the actual filtered response evaluated on a logarithmic frequency axis:

where n _t , « ₇ are the ω _log indices at the initial and final frequencies where the error is evaluated; and ωi _og IA] represents the element k of the vector ω _log .

Figure 2 shows the error responses according to the definition from the equation above for the linear FIR filters shown in Figure 1, also scaled to 10 dB for clarity. To the right of each curve, the measured value of e _log _ _{dB is shown} . The upper curve is the difference between the objective response and the response of the original unfiltered speaker. The average unfiltered error e _{] os} _ _dB is 3.09 dB. With a linear FIR filter of order 100 (the second curve), the error for high frequencies above 5 kHz is very small, but at low frequencies the error reaches up to 12 dB at 40 Hz. The value of e _log _ _dB Low to 2.02 dB. With order 250, the equalization is excellent for frequencies above 2 kHz, but at 40 Hz the error still reaches 8 dB, obtaining an error value ^e \ o _g -dB ^of 1.06 ^dB - ^{With an order of 50} °. ^e ι _og -dB ^ba J up ^to 0.42 dB, obtaining a perfect equalization between 400 Hz and 20 kHz. Finally, with an order 1000, and _log _ _dB decreases to 0.23 dB, there is a residual error in the response at low frequencies that reaches a maximum of 1.95 dB. The problem of linear FIR filters consisting in the poor equalization of the low frequencies is clearly observed in the error responses. Psycho-acoustic studies about perception (FE Toóle, SE Olive, "The modification of timpre by resonantes: perception and measurement", J. Audio Eng. Soc. 36 (3), 1988, 122-142) have determined that a Error less than 1 dB from the objective response is not detectable by most humans when listening to music or voices. In this example, even with a 1000 order, a target deviation of less than 1 dB is not achieved.

Deformed FIR digital filters

Deformed digital filters are achieved by replacing the delay elements in the structure of a digital filter with first-order step-all filters. Oppenheim et al. (AV Oppenheim, DH Jonson, and K. Steiglitz, "Computation of spectra with unequal resolution using the Fourier transform phase", Proc. IEEE, 89 (1971) 299-301) proposed for the first time the possibility of obtaining a frequency resolution not uniform with the Fourier transform. In digital filters, the use of step-all filters instead of the delay elements was proposed by first time by Strube (HW Strube, "Linear prediction on a warped frequency scale", J. Acoustic. Soc. America, 68 (4), 1980, 1071-1076). The first-order step-all filter is defined by equation (5):

A (z) = ^ - ≠ _τ (5)

1 - A ^• z

where λ is the deformation parameter.

The structure of a deformed FIR filter is shown in Figure 3, while Figure 4 shows the structure of the deformed FIR filter proposed by Karjalainen that saves memory and operations (M. Karjalainen, E. Piirilá, A.

Járvinen and J. Huopaniemi. "Comparison of loudspeaker equalization methods based on DSP techniques", J. Audio Eng. Soc. 47 (1/2), 1999, 14-31). The transfer function of a deformed FIR filter is:

Deformed filtering is not a method of designing filters, but a structure that produces the effect of distorting the frequency axis. The filter could be designed using any of the known filter design methods.

The substitution of z ^"1 for A (z) generates the deformation of the frequency axis, which is a function of the phase response of A (z). For a given sampling frequency f _s , the new frequency axis after The deformation is:

L _a ΛfJ _s Λ) (7)

Figure 5 shows the graph of correlation between frequencies due to the effect of deformation. For positive values of 0 <λ <1, the frequency axis is compressed towards high frequencies, and for negative values -1 <λ <0, it is compressed towards low frequencies.

To counteract the lack of resolution at low frequencies of linear FIR filters, deformed filters have been used for equalizing speakers with positive values of λ to shift the high frequencies up and thus achieve a better resolution. Karjalainen proposed its use with FIR and HR filters (M. Karjalainen, A. Hármá, Ul, K. Laine, "Realizable warped NR filtres and their properties", Proceedings of ICASSP 97, 1997, 2205-2208), presenting an NR structure realizable, as well as Hármá (A. Hármá, "Implementation of frequency-warped recursive filtres", Elsevier Signal Processing, 80 (3), 2000, 543-548). Recently, the use of Kautz filters (which can be interpreted as a generalization of deformed filters) for speaker equalization (M. Karjalainen, T. Paatero, "Equalization of loudspeaker and room responses using kautz filtres: direct") has also been proposed. least squares design ", AURASIP Journal on advances in signal processing, 2007, n ° 60949). Tyril also mentions the use of filters for low frequency equalization (M. Tyril, JA Pedersen and P. Rubak, "Digital filters for low-frequency equalization", J. Audio Eng. Soc. 29 (1/2), 2001 , 36-43).

The frequency resolution obtained with the distorted FIR filters is obtained as the resolution of the equivalent linear FIR filter multiplied by the derivative of f _waφ with respect to the frequency, as shown in the following equation:

Figure 6 shows the resolution in relative deformed frequency against

The linear resolution in frequency. For positive λ values, the resolution in frequency increases at low frequencies, but decreases at high frequencies. For negative λ values the opposite effect occurs. By increasing the value of λ approaching 1, an improvement of the resolution at low frequencies is obtained, but the loss of resolution at high frequencies begins very soon and is getting worse. The frequency where the resolution of the deformed scale is the same as that of the linear scale is the crossover frequency, f _t p, and its value is obtained by equation 9. Smith and Abel developed an expression to determine the λ value that best approximates the psychoacoustic scales of Bark and ERB (JO Smith, JS Abel, "Bark and ERB bilinear transform, IEEE", Tras. Speech Audio Processing, 7, 1999, 697-708).

Λ, = ^ - arccos (λ) (9)

L - K

As can be seen in Figure 3, deformed FIR filters require a higher computational cost with respect to a linear FIR filter of the same order. Depending on the architecture of the DSP or microprocessor used, its computational cost increases a factor between 3 and 4 with respect to a linear FIR filter. However, deformed FIR filters can reduce the order of the filter by a factor of up to 5, and therefore their use could be efficient from a computational point of view. Assuming only a penalty factor of 3, the same equalizations of the linear FIR filters of Figure 1 have been made, but this time in distorted FIR filters of an order one third lower than that of the linear FIR filters to maintain the same cost computational In this case, a value of λ of 0.766 has been used to achieve a resolution close to the Bark scale. The equalizations are shown in Figure 7 scaled ten dB for clarity, and the error responses and the value e _log _ _dB are shown in Figure 8. With an order of 33, the distorted FIR filter achieves an error value e _{] 0S} _ _dB of _1.29 dB, better than the 2.02 dB obtained with the linear FIR filter of order 100. Although the equalization at high frequencies is clearly worse due to the reduction in resolution, the equalization at low and medium frequencies it is better, as it can be seen in The error curves of Figures 2 and 8. The error drops to 0.77 dB with an order 83, instead of the 1, 06 dB obtained with the FIR filter of order 250. The error is within the band ± 1 dB from 200 Hz to 20 kHz. For an order of 167, the value _{Xog_} _dB is only 0.12 dB, even better than the equalization achieved with the linear FIR filter of order 1000 (0.23 dB). Finally, with an order of 333, the result is excellent, with a residual error of only 0.03 dB. For the selected λ value, the maximum resolution of the distorted FIR filter around 2 kHz is obtained, getting worse for lower and higher frequencies.

With this comparison, it is clear that the use of deformed filters for speaker equalization can be computationally efficient, expanding the resolution of the filter designed taking into account psycho-acoustic aspects of the human ear. For the same computational cost, better equalizations could be achieved with the use of deformed structures, or a less computational cost would be needed for the same quality of equalization.

Thus, after the analysis of the results shown in the previous paragraphs, in the present example linear FIR filters are combined with deformed FIR filters, as shown in Figures 9 and 10. In Figure 10 a parallel combination of several FIR digital filters deformed with a linear filter. In this example, only the cascade structure of Figure 9 will be analyzed, specifically for FIR filters, although the results are also valid for HR filters. The equalization filter of FIG. 9 is obtained by cascading one or more deformed FIR filters of order N _w ¡and deformation parameter λ¡ with a linear FIR filter of order N. The linear FIR filter will equalize the high and medium frequencies , while deformed FIR filters will equalize the medium and low frequencies. To achieve this, a correct selection of the values of λ¡ must be made to maximize the resolution of the combined filter in the entire frequency band. In the simplest case of using only a distorted filter, the equivalent order of the NMAC filter (in terms of computational cost or MACS) could be approximated as:

where a penalty factor of 3 has been taken for the deformed FIR filter. To reduce the computational cost of the filter, the order of the deformed FIR filter must be as low as possible, since it requires three times the number of MACS than the linear FIR filter.

The frequency resolution of the proposed filter H _f ι _tro (z) will be a combination of the linear resolution of the linear FIR filter H _FIR (Z) and the non-linear resolution of the deformed FIR filter H _WFI R (Z). Figure 11 shows the frequency resolution of linear and distorted FIR filters in terms of the corresponding Q value. This Q value is defined as the ratio between the frequency to be considered and the resolution in frequency of the filter at that frequency:

^Q -i _f ⁽¹¹ >

Thus, for digital filters linear linear (equation 12) and deformed (equation 13), the value of the resolution Q is obtained:

i llJJFF ~ f / \ '¿)

/ N

Figure 12 shows another representation of the resolution, this time in terms of the bandwidth of the resolution in octaves (BW _0Ct ). The bandwidth in octaves is related to Q through the following expression (equation 14), valid for high Q values: BW _^ = (14)

Q Λn {2)

Figures 11 and 13 are evaluated in a logarithmic axis, both in abscissa and ordinates. In this way, the measurement obtained will take into account the natural behavior of the human ear and will serve to judge the resolution in frequency of the filters from a psycho-acoustic point of view.

The resolution of the linear FIR filter, as shown in Figure 12, is constant with a bandwidth of 100 Hz corresponding to a filter order of 480 when a sampling frequency of f _s = 48kHz is used. The resolution of the distorted FIR filter corresponds to a distorted filter of order 480. These resolutions are also compared with a constant resolution of one third octave, and with the resolution in frequency of the Bark scale. From a psycho-acoustic point of view, the comparison of the resolution of deformed filters with the Bark scale is interesting, since it follows the bandwidth of the resolution of the human auditory system using the concept of critical bands (JO Smith, JS Abel , "Bark and ERB bilinear transform, IEEE", Tras. Speech Audio Processing, 7, 1999, 697-708).

For the linear FIR filter, the resolution value Q (and its logarithmic resolution) increases with the frequency, as seen in Figures 11 and 12 for the linear case. The thin dashed lines represent the resolution of a scale of one third octave, which is constant with the frequency. Its resolution value Q is 4.32, and its octave value is obviously 0.333. It is approximately the resolution obtained with a graphic equalizer of one third octave which, for frequencies below 430 Hz, is even better than that obtained with the linear FIR filter of order 480. The dashed dotted lines are the resolutions of The Bark scale calculated from the published frequencies. Up to 500 Hz, its resolution is constant and equal to 100 Hz, as the FIR filter in the example. Above 500 Hz, its behavior is more logarithmic, similar to one third octave, reaching a resolution maximum close to a fifth octave (Q = 6.3) at 2 kHz.

The thick continuous line represents the frequency resolution of the distorted FIR filter of order 480 with a value λ of 0.76 that corresponds to the value that best fits the Bark scale (for f _s = 48 kHz), and is the one that is used in the equalizations of the distorted FIR filter of Figure 7. The shape of the Bark scale (with better resolution) is deduced, with a maximum resolution value Q close to 2 kHz, as shown in Figures 7 and 8. Finally , The thick dashed line represents the resolution of the same distorted FIR filter of order 480 but with λ = 0.95. For both deformed filters, the maximum Q is the same, but the frequency with higher resolution decreases from 2 kHz (λ = 0.76) to 350 Hz (λ = 0.95). Also, the resolution at low frequencies has been multiplied by 4.5 in the second case, the same factor according to which the resolution at high frequencies has decreased.

The two graphs of Figures 11 and 12 demonstrate that with an appropriate selection of the λ value it is possible to select the frequency band where the distorted FIR filter achieves the best resolution. In other words, it is possible to adjust the resolution of the filter. In the filter structure proposed in this patent application for the equalization of loudspeakers, the use of deformed FIR digital filters of low orders is effective to reduce the computational cost, with values of λ greater than 0.9 to achieve resolution at low frequencies

To better understand the effect of the variation of the parameter λ, an example is shown below. The previously used speaker has been equalized with two filters of order N _w = 33 and λ values of 0.76 and 0.95. Their results are shown in Figure 13. As mentioned above, with λ = 0.76 the maximum resolution of the filter is approximately 2 kHz, obtaining a poor equalization at low and high frequencies. When λ = 0.95 (centered on -10 dB for clarity) is used, the equalization of the low frequencies is improved at the expense of worsening the equalization of the frequencies high. The maximum resolution of the filter is now around 350 Hz, obtaining an error of less than 1 dB for 20 Hz up to 1.5 kHz with an order of only 33, which is equivalent to a computational cost equivalent to a linear FIR filter of order 100. The error responses of the two equalizations are shown in Figure 14, where it can be seen how the maximum resolution of the filters changes with the two values of λ.

To facilitate the selection of the appropriate λ value, the frequency of the maximum resolution Q is represented as a function of λ for different sampling frequencies: 44.1, 48, 88.2 and 96 kHz. The graphs in Figure 15 show these results between 20 Hz and 6 kHz for λ values from 0.7 to 1. The left-most curve corresponds to a fs of 44.1 kHz, and the one on the most right to 96 kHz With these graphs, it is easy to choose the value of λ to adjust the stress of the distorted FIR filter in frequency.

The selection of the three parameters (order N of the linear FIR filter, order Nw of the deformed FIR filter and λ value for the deformed FIR filter) for the specific equalization of a filter must be based on a compromise between the demand for equalization at low frequencies (for the selection of N _w and K), and at medium and high frequencies (for N).

In accordance with all of the above, the design of the proposed equalization filter requires the joint design of the linear FIR filter of order N and the filter

Deformed FIR of order N _w and deformation parameter λ. To maintain the requirement of low computational cost, the order of the deformed filter must be

The lowest possible.

Thus, for the design of a cascade filter in which a linear FIR filter follows a deformed FIR filter, the deformed FIR filter is designed first. This stage focuses on equalizing the low frequencies through an appropriate selection of the λ parameter. This selection depends on two factors: the lowest frequency to be corrected (subwoofers) and the order of the second stage filter (the filter Linear FIR), which determines its resolution at low frequency and, therefore, the point of connection between both filters.

Secondly, the linear FIR filter is designed based on the response of the loudspeaker filtered by the first stage. This second stage will correct the response of the distorted FIR filter of the first stage mainly at high frequencies. This linear FIR filter does not have to correct the low frequencies because they have been previously corrected by the deformed FIR filter.

The order of the two filters is related to the precision required in the equalization and is conditioned by the available computational cost. Figure 13 shows the results that can be achieved in the example speaker using a distorted FIR. Using N _w = 33 and λ = 0.95 it is possible to achieve an error of less than 1 dB up to 1.5 kHz. Figure 2 shows that it is also possible to achieve an error below 1 dB at high frequencies (1.5 kHz to 20 kHz) with a linear FIR filter of order N between 100 and 150. According to the previous equation , an equivalent order NMA _C filter of 200 to 250 will be obtained, with a residual equalization error of less than 1 dB in the entire audio frequency band. To achieve this level of equalization, a linear FIR filter of more than an order greater than 1000 is needed, as shown in Figure 2. If a deformed FIR filter is used, an order Nw = 167 (N _MA C = 500), as seen in Figure 8. Therefore, computational cost can be saved using the proposed topology, compared to existing topologies that use only linear FIR filters or deformed FIR filters.

For example, it is desired to equalize the speaker whose output is shown in Figure 16 on the 0 dB line. It also represents the level 0 dB Ia target frequency response H _Objet _vo (ω). The response of the original error is represented in Figure 17, the initial error being _{Xo &} _ _dB of 3.09 dB. Its maximum error is 12 dB at 40 Hz and it has several peaks and valleys of more than 4 dB throughout the entire audio frequency band. The results of the equalizations are shown in Figure 16, and the error graphs and values of _{Xoa_} _dB are shown in Figure 17.

Example 1

Using the proposed structure, a filter of an equivalent order NM _A C = 250 will be designed, composed of a deformed FIR filter of order N _w = 33 and a FIR filter of order N = 151. The first operation in the design of the proposed filter is to design the deformed FIR filter with a λ value selected so that sufficient equalization is achieved at low frequencies. In this case, a value of λ = 0.98 has been used, which corresponds to a frequency with a maximum resolution of 150 Hz when a sampling frequency fs = 0.48 is used, as can be seen in Figure 15. With these values of N _w and λ, the equalization that is achieved is the one shown in Figure 16 on the level of -10 dB, which is quite good up to 700 Hz (with an order of only N _w = 33) . The error curve is shown in Figure 17 and is below 0.4 dB up to 700 Hz, and _[og _ _dB = 0.98 dB. Once the deformed FIR filter has been designed, the linear FIR filter of order N = 151 is designed from the response filtered by the deformed FIR. The combined equalization that is achieved is shown on the level of -20 dB in Figure 16, and the residual error in Figure 17, with an error value e _Xog _ _dB = 0.08 dB. The linear FIR filter corrects the response at high frequencies up to 2.5 kHz in an excellent way, with an error curve below 0.1 dB. Between 700 Hz and 2.5 kHz, the equalization is somewhat worse, but the error is always less than 0.8 dB. This is the frequency band in which neither the linear FIR filter nor the deformed FIR filter achieve a sufficient resolution with the selected filter orders. However, from a practical point of view, the equalization obtained will not be distinguishable from a better one by most users, as can be seen from multiple experiments related to the human ear.

If we assume that an error curve below 1 dB in the entire audio band (from 20 Hz to 20 kHz) is acceptable for equalization, the order equivalent of the NMA _C filter could be reduced even up to 100, with N _w = 11 and N = 77. The equalization obtained and the error responses are above the -30 dB lines in Figures 16 and 17, with an e _{] og} _ _dB = 0.28 dB.

With the proposed filter, it is possible to achieve that level of equalization with a computational cost of only 100 MACS, obtaining a more uniform frequency resolution, when evaluated on a logarithmic frequency axis, than that obtained when only linear FIR filters are used or deformed FIR filters.

Example 2

In this example, another speaker is equalized, consisting of a 5-inch woofer and a ³ -inch tweeter. Its frequency response is shown with a thick line in Figure 18 above the 0 dB level. The objective response that is represented with a thin line has been chosen. The equalization obtained with NMAC = 250 (N _W = 33, N = 151, λ = 0.96) is shown centered on the level of -10 dB. The error curve is always below ± 0.5 dB from 40 Hz to 20 kHz.

Comparison

The results obtained by equalizing the loudspeaker of the first example are then compared using the proposed filter with the results when a linear FIR filter or a separately deformed FIR filter is used. The comparison is carried out using the same computational cost for the three filters, in this case 250 MAC. Figure 19 shows the frequency response of the speaker, the objective response and the responses after equalization, scaled from ten to ten dB for clarity. The respective error and _log _ _dB responses are shown in Figure 20, with an original error value of e _M = 3.09 dB.

The linear FIR filter of order 250 is represented on the line of -10 dB, getting an equalization error curve that is within ± 1 dB from 200 Hz to 20 kHz, but at low frequencies the error reaches 7.5 dB at 40 Hz. The resulting error value is e _λog _ _dB = 1.06 dB.

The deformed FIR filter, shown on the line of -20 dB, has an order Nw = 83, which corresponds to an equivalent order NMA _C = 250 (assuming a penalty factor of 3 for the deformed implementation of the filter). In this case, the value of λ selected is 0.76, the maximum resolution of the filter being around 2 kHz. The error is now below ± 1 dB between 150 Hz and 10 kHz, but is greater at higher and lower frequencies. The error value is better than with the linear FIR filter, and _iog _ _dB = 0.77 dB.

Finally, the equalization with the proposed filter structure is represented on the -30 dB line. It has NMAC = 250, with a distorted FIR filter of N _w = 33 with λ = 0.98 and a linear FIR filter with N = 151. The error curve is within ± 1 dB from 20 Hz to 20 kHz, and even below ± 0.5 dB between 20 Hz and 800 Hz and between 1.5 kHz and 20 kHz. The error value is only ^e i _oS - _d β = ° ^'08 dB, which indicates that from a psycho-acoustic point of view, the perceived error will be the smallest of the three filters. With the same computational cost, the proposed filter obtains a flatter equalization and a lower error value, thus requiring a lower order filter to achieve a value of the desired error in the equalization.

Finally, Figure 21 shows the scheme of an apparatus (1) for the digital filtering of signals according to the present invention, in which the different elements that compose it are appreciated. In an example of speaker equalization (not shown), the input signal to the device (1) already arrives in digital format, and therefore is received by the input means (11) through the digital frame receiver (2) . The input means (11), in turn, sends it to the processing medium (6), which performs all the operations necessary to apply the digital filtering according to the invention. Finally, the already filtered signal leaves the device (1) through the digital frame transmitter (3), which it is included in the outlet means (12).

The input and output means (11 and 12) of the apparatus (1) of this example further comprise analog / digital (4) and digital / analog converters (5), necessary when the signal to be filtered is initially in analog format or when I must send in that format. Additionally, the apparatus (1) comprises a memory unit (7) for storing results or characteristics of the input signal to the apparatus or of the filtered signal calculated by the processing means (6), a communications medium (8), which allows the sending of information, an interface means (10) for the interaction between the device (1) and the users, and a microcontroller (9) that manages the operation of the previous elements.

Claims

1. Digital signal filtering method characterized in that it comprises applying a linear digital filtering combined with at least one deformed digital filtering to obtain an objective response to a response signal of a system.

2. Digital signal filtering method according to claim 1, characterized in that the operation of applying a linear digital filtering combined with at least one deformed digital filtering is performed according to a cascade scheme .

3. Digital signal filtering process according to claim 1, characterized in that the operation of applying a linear digital filtering combined with at least one deformed digital filtering is performed according to a parallel scheme.

4. Digital signal filtering method according to any of the preceding claims, characterized in that the system is an acoustic system.

5. Digital signal filtering process according to claim 4, characterized in that the acoustic system is a loudspeaker.

6. Digital signal filtering method according to claim 4, characterized in that the acoustic system is a hearing aid.

7. Computer program comprising program instructions that cause a computer to carry out the operations of the method according to any of the preceding claims.

8. Computer program according to claim 7, characterized because it is stored in storage media.

9. Computer program according to claim 7, characterized in that it is transmitted through a carrier signal.

10. Apparatus (1) for digital signal filtering, characterized in that it comprises:

an input means (11), which transmits an input signal to a processing means (6);

a processing means (6), which receives the input signal from the input means (11) and Ie applies a digital filtering that combines a linear filtering with at least one deformed filtering, obtaining an objective signal.

11. Apparatus (1) for digital signal filtering according to claim 10, characterized in that the processing medium (6) is chosen from the following list: a computer, a DSP, an FPGA, an ASIC, a microprocessor and a microcontroller.

12. Apparatus (1) for digital filtering of signals according to any of claims 10 or 11, characterized in that it further comprises an output means (12), which transmits the target signal from the processing medium (6) to the outside .

13. Apparatus (1) for digital signal filtering according to any of claims 10-12, characterized in that the input and output means (11, 12) respectively comprise analog-digital conversion means (4) and digital-analog (5) and / or a receiver (2) and a digital data transmitter (3).

14. Apparatus (1) for digital filtering of signals according to any of claims 10-13, characterized in that it further comprises a means of communications (8).

15. Apparatus (1) for digital signal filtering according to any of claims 10-14, characterized in that it further comprises an interface means (10) with the users.

16. Apparatus (1) for digital filtering of signals according to any of claims 10-15, characterized in that it further comprises a storage medium (7).

17. Apparatus (1) for digital signal filtering according to any of claims 10-16, characterized in that it further comprises a microcontroller (9).