ES2341200B2 - PROCEDURE AND APPLIANCE FOR DIGITAL SIGNAL FILTERING. - Google Patents

Abstract

Procedure and apparatus for digital filtering of signals.

The main object of the present invention is a procedure and an apparatus for digital signal filtering applicable to fields such as audio, video, communications, radar, seismology etc., which allows to achieve an excellent resolution spectral in a wide range of frequencies. In addition, you get a great computational savings in relation to digital filters employees so far. Fundamentally, the procedure includes using a combination of linear digital filters with Deformed linear filters, either cascaded or parallel. The invention is especially useful in the field of acoustics.

Description

Procedure and apparatus for digital filtering of signals.

Object of the invention

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

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Background of the invention

Digital signal filtering is widely employed in different fields, such as audio, video, communications, radar, seismology, etc. In this document we will name "equalization" to a filter whose objective is to improve or compensate for the non-ideal response of a system by filtering of your complex response with the filter designed so that the Filtered response resembles an objective response. For him 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 about an analysis".

On the other hand, in this document we will call the system whose response you want to call "system" filter. Examples of systems can be a speaker, a radar, channel of communications, etc. The following equation relates the function ideal transfer filter to design with the function of objective transfer and transfer function of the system:

one

When the system transfer function is not of minimum phase, its inverse will be unstable, so the transfer function of the filtered system may only approximate The objective transfer function.

In recent years, various methods for the design of digital filters. However, when the frequency band to equalize or analyze covers a wide range octaves (for example, three or higher), all these methods require a high computational cost to get a spectral resolution in proper equalization across the entire range of frequencies

Linear digital filters get a excellent resolution at high frequencies, but poor 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 linear filter is implemented in the time domain The computational cost is lower if implemented in the frequency domain by Fourier transform (FFT, Fast Fourier Transform in English). However, this solution introduces a latency, due to storage processes in buffer at the entrance and exit, which can limit its use in Real-time applications that require low latency. In audio applications, for example, this latency can result 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, may be higher at low frequencies at cost of losing it at high frequencies. However, one of the major drawbacks of warped or warped filters consist in the increase of the computational cost.

Therefore, there is a need for a filter digital that has a good resolution at both high and low frequencies, and that does not involve excessive computational cost or Enter latencies not allowed.

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Description of the invention

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

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

The equation that defines the function of Transfer of a linear FIR digital filter is as follows:

2

where N is the order of filter.

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On the other hand, a digital FIR filter is obtained warped or warped when the unit elements of delay z <-1> of a linear FIR digital filter by filters step-all first order. Therefore the function transfer of a deformed FIR digital filter is the next:

3

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 (\ lambda <0).

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

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

4

On the other hand, to obtain the function of transfer of a deformed IIR digital filter, the unit delay elements z <-1> by pass filters- all of first order and the coefficients a_ {i} by the new coefficients \ sigma_ {i}:

5

Therefore, and according to an aspect of the present invention, a filtering process is provided digital comprising applying to the response signal of a system a linear filtrate combined with at least one deformed filtrate to get an objective response, which is chosen based on each application.

To do this, first the signal is obtained System response For example, for the equalization of a speaker, you could calculate the response using techniques such as MLS (Maximum Length Sequence), sinusoidal scanning Logarithmic or periodic noise. However, it is also possible assume, based on experience, that the response signal from the system that you want to equalize has certain features. For example, to provide speakers different equalizations depending on the type of music played normally the response signal of the speakers is not calculated, but that a series of characteristics common to all speakers. Still another possibility is to apply the procedure of digital filtering to a transmitted signal, without knowing or have access to the system that originated the signal. Therefore, in this scope the term "the response signal of a system" makes Reference to all these possibilities.

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

The procedure, in addition to producing savings important computational regarding filtering procedures known, it is effective at both low and high frequencies, but to obtain optimal results should be applied to signals that cover a range of octaves around three or higher. For another On the other hand, it is obvious to a person skilled in the art that a combination, in cascade or in parallel, linear digital filters can be Simplify in a single linear digital filter. For this reason, the term "a linear filter" or "a linear filter" used herein also covers combinations of linear filters

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

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

- the parallel combination of a filtrate linear and, at least, a deformed filtrate.

A preferred application of the invention is aimed at filtering acoustic systems, understood as such any device intended for sound reproduction, both in the final stage of reproduction as in any intermediate stage of Signal treatment or amplification. Preferred embodiments of the procedure aimed at acoustic systems would be the cases of its application to speakers or headphones.

According to another aspect of the invention, it also extends to computer programs, in particular computer programs in a carrier content, adapted to carry out the operations of the described procedure. He program can be in the form of source code, object code or a intermediate code between the source code and the object code, such as a partially compiled form, or any other suitable form 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 hard drive. In addition, the carrier can be a transmission carrier, such as an electrical or optical signal that is can communicate via electrical, optical, radio or radio cable any other way.

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

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

- A processing medium, which receives the signal of input of the input medium and performs a digital filtering that combines a linear filtrate with at least one deformed filtrate. He processing medium can be of any type capable of carrying perform the digital filtering procedure that combines a filtrate linear digital with at least one deformed digital filtering of in accordance with what was previously described in this document, although according to preferred embodiments, it can be a DSP, an FPGA, a ASIC, a microprocessor or a microcontroller. In addition, in case of applications in signal analysis, the processing medium is able to perform the calculations required to extract the analysis information, such as calculating characteristics as average, effective values, graphics development, etc.

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

According to preferred embodiments of the invention, the apparatus for digital signal filtering comprises also a means of communications. The communications medium can be any means that allows the device to be connected to a computer or any other external system to transfer parameters from configuration of the filtrate to be implemented, results or graphics calculated by the processing means or any other type of information.

According to a preferred embodiment more than the invention, the apparatus for digital signal filtering It comprises a means of interface with users, which allows these modify filtering parameters. Another function of the medium of interface can be the visualization of results or graphs calculated by the processing means. The interface medium it could be, for example, a touch screen or a keypad.

According to another preferred embodiment of the invention, the apparatus for digital signal filtering comprises also a storage medium, where data is stored relative to equalized signals or filtering parameters. The storage medium could be any of those known in the technique, such as a hard disk, a CD, a DVD, etc.

Finally, according to an embodiment more preferably of the present invention, the apparatus for filtering Digital signal comprises a microcontroller, which controls the operation of the interface and communications media.

Description of the drawings

To complement the description that is being performing and in order to help a better understanding of the characteristics of the invention, according to an example preferred practical implementation of it, is accompanied as integral part of that description, a set of drawings where with an illustrative and non-limiting nature, what has been represented next:

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

Figure 2.- Graph showing the error responses (scaling from ten to ten decibels) and the e log-dB value of linear FIR filters.

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

Figure 4.- Graph showing a structure optimized deformed FIR filters.

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

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

Figure 7.- Graph showing the equalization with distorted FIR filters of order one third smaller than filters Respective linear FIRs, with λ = 0.766 and f_ {s} = 48 kHz.

Figure 8.- Graph showing the error responses and the e log-dB value for the distorted FIR filters.

Figures 9 and 10.- Represent structures Possible filter according to the present invention: 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 distorted FIR filters of order 33 for two values of λ.

Figure 14.- Graph showing the response of the error relative to the filters in the previous graph.

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

Figure 16.- Graph showing the equalization obtained with the proposed filter structure for N_ {MAC} = 250 and 100

Figure 17.- Graph showing the error responses and the e log-dB values obtained with the filter structure according to the present invention for N MAC = 250 and 100.

Figure 18.- Graph showing the equalization from speaker 2 with N_ {MAC} = 250.

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

Figure 20.- Graph showing a comparison between error responses and e -log-dB values.

Preferred Embodiment of the Invention

As explained above herein document, an example is now shown in which the procedure of the present invention to equalization of speakers, using a combination of digital FIR filters linear and deformed, showing that the combination of both offers optimal results for equalization of signals from audio, using a low computational cost without Enter latency in the operation. These results are presented. here merely by way of example, 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 of FIR type. Specifically, in this example a loudspeaker of the RAMSA brand (Panasonic) that has a 8-speaker bass inches in bass-reflex configuration, and a 3/4 inch tweeter for treble.

Linear FIR digital filters

First, the behavior of linear FIR digital filters is shown. Figure 1 shows the equalization results of a passive speaker with an 8-inch woofer for low frequencies and a ¾ 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. Vol. 42, no. 11, pp 884-900, Nov. 1994). The upper graph, centered at 0 decibels (dB) shows the response of the unfiltered loudspeaker H (Ω) and the objective response H objective (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 speaker's natural pass-band response, extending its response at low frequencies in a reasonable manner without introducing 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 equalization at high frequencies is excellent for any order, but deficient at low frequencies, although it improves with the order of the filter.

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The low resolution observed in the axis of logarithmic frequencies at low frequencies of FIR filters linear is due to the linear treatment of the frequency axis in the design and implementation of the filter, either in the time domain or of the frequency. The frequency resolution of an FIR filter is define approximately as follows:

6

where

\ Delta f {FIR} is the frequency resolution;

f s is the sampling frequency; Y

N is the order of the filter.

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With a sampling frequency of 48 kHz, for an order of 100 a resolution of 480 Hz is obtained, for 250 it you get 192 Hz, for 500 you get 96 Hz, and for 1000 you get 48 Hz. These resolutions are sufficient for equalization of speakers at high frequencies, but not for low frequencies in the that 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 over 10,000 to get this resolution, with the immense computational cost that it required if implemented in the time domain. To reduce the computational cost, it is possible to filter in the domain of the frequency using FFT, but at the expense of increasing the latency to inadmissible extremes in applications where delays of more than 10 milliseconds are annoying for musicians or speakers (S. E. Olive, F. E. Toole, "The detection of reflections in typical rooms ", J. Audio Eng. Soc. 37 (7/8), 1989, 539-553).

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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. Given this behavior, psycho-acoustic scales such as Bark and ERB have been developed (M. Karjalainen, E. Piirilä, A. Järvinen 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 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 e log-dB estimator has been defined (G. Ramos, JJ López, "Filter design method for loudspeaker equalization base don IIR parametric filtres" , J. Audio Eng. Soc. 54 (12), 2006, 1162-1178). The frequency axis is logarithmically discretized to form the vector \ omega_ {log} (equation 2), which has a resolution of 1/48 octave, obtaining 576 frequencies between 5 Hz and 20 kHz, which is sufficient for equalization.

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

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Below is the expression that defines the estimator e log-dB (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:

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9

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where

n _ {i}, {f} _ n are indices \ omega_ {log} to start and end frequencies where the error is evaluated; Y

\ omega_ {log} [ k ] represents the element k of the vector \ omega_ {log}.

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Figure 2 shows the error responses according to the definition of 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 target response and the original unfiltered speaker response. The average error unfiltered ei {log-dB 3.09 dB} is. 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 e log value -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 log-dB of 1.06 dB. With an order of 500, e log-dB falls to 0.42 dB, obtaining a perfect equalization between 400 Hz and 20 kHz. Finally, with an order 1000, e 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 of poor equalization of low frequencies is clearly seen in the error responses. Psycho-acoustic studies on perception (FE Toole, 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 target 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.

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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 delay elements was first proposed 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):

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where \ lambda is the parameter of deformation.

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

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

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The substitution of z <-1> with A (z) generates the deformation of the frequency axis, which is a function of the phase response of A (z). For a sampling frequency f_ {s} given, the new frequency axis after deformation is:

12

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

To counteract the lack of resolution to low frequencies of linear FIR filters, filters have been used deformed for speaker equalization with positive values of λ to shift the high frequencies up and get a better resolution. Karjalainen proposed his use with FIR and IIR filters (M. Karjalainen, A. Härmä, Ul, K. Laine, "Realizable warped IIR filtres and their properties", Proceedings of ICASSP 97, 1997, 2205-2208), presenting a workable IIR structure, as well as Härmä (A. Härmä, "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 equalization of speakers (M. Karjalainen, T. Paatero, "Equalization of loudspeaker and room responses using kautz filtres: direct least squares design ", AURASIP Journal on advances in signal processing, 2007, no. 60949). Tyril also mentions the use of filters for equalization at low frequencies (M. Tyril, J. A. Pedersen and P. Rubak, "Digital filtres for low-frequency equalization ", J. Audio Eng. Soc. 29 (1/2), 2001, 36-43).

The resolution in frequency that is obtained with deformed FIR filters are obtained as the filter resolution Linear FIR equivalent multiplied by the derivative of f_ {warp} regarding the frequency, as the following shows equation:

13

Figure 6 shows the resolution in frequency relative deformation against linear frequency resolution. 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. To the increase the value of λ approaching 1, you get a Improved resolution at low frequencies, but loss of Resolution at high frequencies begins very soon and is getting worse. The frequency where the resolution of the deformed scale is equal that the linear scale is the crossover frequency, f_ {tp}, 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 (J. O. Smith, J. S. Abel, "Bark and ERB bilinear transform, IEEE", Tras. Speech Audio Processing, 7.1999, 697-708).

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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 by 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 warped 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 λ value 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 e -log-dB value are shown in Figure 8. With an order of 33, the distorted FIR filter achieves a value of 1.29 dB error e log-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, since it can be seen in the error curves of Figures 2 and 8. The error goes down to 0.77 dB with an order 83, instead of the 1.06 dB obtained with the filter FIR of order 250. The error is within the band ± 1 dB from 200 Hz to 20 kHz. For an order of 167, the e log-dB value 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 value λ selected, the maximum resolution of the distorted FIR filter around 2 kHz is obtained, worsening for lower and higher frequencies.

With this comparison, it is clear that the use of warped filters for speaker equalization can be computationally efficient, expanding filter resolution designed taking into account psycho-acoustic aspects of the human ear For the same computational cost, they could achieve better equalizations with the use of structures deformed, or 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 combine linear FIR filters with deformed FIR filters, as shown in figures 9 and 10. Figure 10 shows a parallel combination of several deformed FIR digital filters With a linear filter. In this example, only the cascade structure of figure 9, specifically for FIR filters, although the results are also valid for IIR filters. He equalization filter of figure 9 is obtained by combining in cascade one or more deformed FIR filters of order N_ {Wi} and deformation parameter \ lambda_ {i} with a linear FIR filter of order N. The linear FIR filter will equalize the high frequencies and averages, while deformed FIR filters will equalize the medium and low frequencies. To achieve this, you must perform a correct selection of the values of \ lambda_ {i} for maximize the resolution of the combined filter across the entire band of frequencies In the simplest case of using only one filter deformed, the equivalent order of the N_ {MAC} filter (in terms of computational cost or MACS) could be approximated as:

fifteen

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

The frequency resolution of the proposed filter H_ {filter} (z) will be a combination of linear resolution of the linear FIR filter H_ {FIR} (z) and the non-linear resolution of the deformed FIR filter H_ {WFIR} (z). Figure 11 shows the frequency resolution of linear and deformed FIR filters in terms of the corresponding Q value. This Q value is defined as the quotient between the frequency to consider and the resolution in filter frequency at that frequency:

16

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

17

Figure 12 shows another representation of the resolution, this time in terms of the bandwidth of the resolution in octaves (BW_ {oct}). The bandwidth in octaves is relate to Q through the following expression (equation 14), valid for high Q values:

18

Figures 11 and 13 are evaluated on an axis Logarithmic, both abscissa and ordinate. In this way, the measure obtained will take into account the natural behavior of the ear human 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 using a sampling rate of f_ {s} = 48 kHz. Filter resolution Deformed FIR corresponds to a distorted filter of order 480. These resolutions are also compared with a constant resolution of a third octave, and with the resolution in frequency of the scale Bark From a psycho-acoustic point of view, the comparison of the resolution of deformed filters with the scale Bark is interesting, since it follows the resolution bandwidth of the human auditory system using the concept of bands critics (J. O. Smith, J. S. Abel, "Bark and ERB bilinear transform, IEEE ", Tras. Speech Audio Processing, 7, 1999, 697-708).

For the linear FIR filter, the value of Q resolution (and its logarithmic resolution) increases with the frequency, as seen in figures 11 and 12 for that matter linear. Thin dashed lines represent resolution of a one-third octave scale, which is consistent with the frequency. Its resolution value Q is 4.32, and its octave value It is obviously a 0.333. It is approximately the resolution obtained with a graphic equalizer of a third octave which, for frequencies below 430 Hz, it is even better than the one you get with the linear FIR filter of order 480. The lines dashed points are the resolutions of the Bark scale calculated from published frequencies. Up to 500 Hz, its resolution is constant and equal to 100 Hz, as the FIR filter of the example. Above 500 Hz its behavior is more logarithmic, similar to a 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 λ value of 0.76 corresponding to the value that best suits adjusts to the Bark scale (for f_ {s} = 48 kHz), and is the one that used in the equalizations of the deformed FIR filter of the figure 7. The shape of the Bark scale (with better resolution) is deduced, with a maximum Q resolution value 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) up 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.

The two graphs of figures 11 and 12 demonstrate that with an appropriate selection of the value λ is possible to select the frequency band where the FIR filter Deformed gets 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 equalization of loudspeakers, the use of warped FIR digital filters of orders low 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 variation of the \ lambda parameter, an example is shown below. He previously used speaker has been equalized with two filters order N_ {W} = 33 and λ values of 0.76 and 0.95. Your results 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 frequencies and high. When λ = 0.95 is used (centered at -10 dB per clarity), low frequency equalization is improved to at the expense of worsening the equalization of high frequencies. The Maximum filter resolution is now around 350 Hz, obtaining an error of less than 1 dB for 20 Hz up to 1.5 kHz with a order of only 33, which equals a computational cost equivalent to a linear FIR filter of order 100. The responses of error of the two equalizations are shown in figure 14, where you can see how the maximum resolution of the filters changes with the two values of λ.

To facilitate the selection of the value \ lambda suitable, 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 those results between 20 Hz and 6 kHz for λ values from 0.7 up to 1. The leftmost curve corresponds to an f_ {s} of 44.1 kHz, and the rightmost at 96 kHz. With these graphics, it is easy to choose the value of \ lambda to adjust the frequency FIR filter strain deformed.

The selection of the three parameters (order N of linear FIR filter, order N_ {W} of the deformed FIR filter and value λ for the distorted FIR filter) for equalization specific to a filter should be based on a compromise between the low frequency equalization demand (for the selection of N_ {W} and λ), 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 FIR linear order filter N and deformed order FIR filter N_ {W} and deformation parameter λ. To keep the low computational cost requirement, the order of the filter Deformed should be as low as possible.

Thus, for the design of a cascade filter in which a linear FIR filter follows a deformed FIR filter, in First, the deformed FIR filter is designed. This stage is centered in equalizing the low frequencies through a selection suitable parameter \ lambda. This selection depends on two factors: the lowest frequency to be corrected (subwoofers) and the order of the second stage filter (the linear FIR filter), which determines its resolution at low frequency and, therefore, the point of link between both filters.

Second, the linear FIR filter is designed from the response of the speaker filtered by the first stage. This second stage will correct the response of the deformed FIR filter of the first stage mainly at high frequencies. This linear FIR filter does not have to correct low frequencies because which have already been previously corrected by the FIR filter deformed.

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

For example, you want to equalize the speaker whose output is shown in Figure 16 on the 0 dB line. The target frequency response H_ {target} (\ omega) is also represented on the 0 dB level. The response of the original error is represented in Figure 17, with the initial error e log-dB being 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 e -log-dB values are shown in Figure 17.

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Example one

Using the proposed structure, a filter of an equivalent order N_ {MAC} = 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 proposed filter design 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 f_ {s} = 0.48 is used, as can be seen in Figure 15. With these values of N_ {W} and λ, the equalization achieved is that 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 e log-dB = 0.98 dB. Once the deformed FIR filter is designed, the linear FIR filter of order N = 151 is designed from the response filtered by the deformed FIR. The combined equalization achieved is shown above the level of -20 dB in Figure 16, and the residual error in Figure 17, with an error value e log-dB = 0.08 dB. The linear FIR filter corrects the response at high frequencies up to 2.5 kHz excellently, 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 achieves 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 equivalent order of the N_ {MAC} 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 -log-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 using only linear FIR filters or deformed FIR filters.

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Example 2

In this example another speaker is equalized, Composed of a 5-inch woofer and a ¾ inch tweeter. Your frequency response is shown with a thick line in the Figure 18 above the 0 dB level. The answer has been chosen target that is represented with a thin line. Equalization obtained with N_ {MAC} = 250 (N_ {W} = 33, N = 151, λ = 0.96) is Sample 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 e log-dB error responses are shown in Figure 20, with an original error value of e log-dB = 3.09 dB.

The linear FIR filter of order 250 is represented on the -10 dB line, obtaining a curve of the equalization error 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 log-dB = 1.06 dB.

The deformed FIR filter, shown on the -20 dB line, has an order N_ {W} = 83, which corresponds to an equivalent order N_ {MAC} = 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, with 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, e log-dB = 0.77 dB.

Finally, equalization with the proposed filter structure is represented on the -30 dB line. It has N_ {MAC} = 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 log-dB = 0.08 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 digital signal filtering according to the present invention, in which the different elements are appreciated That composes. In an example of speaker equalization (no shown), the input signal to the device (1) arrives in format digital, and therefore is received by the input means (11) to through the receiver of digital frames (2). The means of entry (11), in turn, sends it to the processing medium (6), which performs all the operations necessary to apply digital filtering of according to the invention. Finally the already filtered signal leaves the apparatus (1) through the digital frame transmitter (3), which it is included in the outlet means (12).

The means of entry and exit (11 and 12) of the apparatus (1) of this example further comprise converters analog / digital (4) and digital / analog (5), required 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 device or the signal filtered calculated by the processing means (6), a means of communications (8), which allows the sending of information, a means of interface (10) for the interaction between the device (1) and the users, and a microcontroller (9) that manages the operation of the previous elements.

Claims (15)

1. Digital signal filtering process characterized in that it comprises applying a cascade or parallel combination of a linear digital filtering with at least one deformed digital filtering to obtain an objective response, and where the Filter combination does not include any delay. 2. Digital signal filtering method according to claim 1, characterized in that the system is an acoustic system. 3. Digital signal filtering method according to claim 2, characterized in that the acoustic system is a loudspeaker. 4. Digital signal filtering method according to claim 2, characterized in that the acoustic system is a hearing aid. 5. Computer program comprising program instructions that cause a computer to perform the operations of the procedure according to any of the previous claims. 6. Computer program according to claim 5, characterized in that it is stored in storage media. 7. Computer program according to claim 5, characterized in that it is transmitted through a carrier signal. 8. Apparatus (1) for digital signal filtering, characterized in that it comprises: an input means (11), which transmits a input signal to a processing medium (6); Y a processing means (6), which receives the input signal of the input medium (11) and a filter is applied digital that combines linear filtering with at least one filtering deformed, in cascade or in parallel, obtaining an objective signal, where the combination of filtrates does not include delays. 9. Device (1) for digital signal filtering according to claim 8, 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. 10. Apparatus (1) for digital signal filtering according to any of claims 8 or 9, characterized in that it further comprises an output means (12), which transmits the target signal from the processing medium (6) to the outside . 11. Apparatus (1) for digital signal filtering according to any of claims 8-10, 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). 12. Apparatus (1) for digital filtering of signals according to any of claims 8-11, characterized in that it further comprises a communications medium (8). 13. Apparatus (1) for digital signal filtering according to any of claims 8-12, characterized in that it further comprises an interface means (10) with the users. 14. Apparatus (1) for digital filtering of signals according to any of claims 8-13, characterized in that it further comprises a storage medium (7). 15. Apparatus (1) for digital signal filtering according to any of claims 8-14, characterized in that it further comprises a microcontroller (9).