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WO1992005501A1 - Systeme et procede de production d'un filtre numerique a reponse impulsionnelle finie adaptatif a resolution de frequence non lineaire - Google Patents

Systeme et procede de production d'un filtre numerique a reponse impulsionnelle finie adaptatif a resolution de frequence non lineaire Download PDF

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Publication number
WO1992005501A1
WO1992005501A1 PCT/US1991/006846 US9106846W WO9205501A1 WO 1992005501 A1 WO1992005501 A1 WO 1992005501A1 US 9106846 W US9106846 W US 9106846W WO 9205501 A1 WO9205501 A1 WO 9205501A1
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WO
WIPO (PCT)
Prior art keywords
filter
coefficients
frequency
adaptive
equalization
Prior art date
Application number
PCT/US1991/006846
Other languages
English (en)
Inventor
Ronald P. Genereux
Original Assignee
Cambridge Signal Technologies, Inc.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Cambridge Signal Technologies, Inc. filed Critical Cambridge Signal Technologies, Inc.
Publication of WO1992005501A1 publication Critical patent/WO1992005501A1/fr

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Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H21/00—Adaptive networks
    • H03H21/0012—Digital adaptive filters
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H21/00—Adaptive networks
    • H03H21/0012—Digital adaptive filters
    • H03H2021/0096—Digital adaptive filters with input-sampling frequency and output-delivery frequency which differ, e.g. extrapolation; anti-aliasing

Definitions

  • the present invention relates to a filtering system and more particularly to an equalization system and method for utilizing adaptive digital filters with non-linear frequency resolution.
  • Quality audio products are designed with the goal of reproducing as accurately as possible at the
  • Room boundaries can have a significant effect on the sound radiated by a loudspeaker and eventually perceived by the listener. Reflections off walls and furniture combine at the listener's ears in a complex manner such that the various frequency components in the music are unbalanced, influencing the sound to a greater extent than any other component in the system. The problem is difficult to deal with because the extent of the problem can only be assessed by making a measurement of the system at the exact listening position.
  • a solution to the problem is to use adaptive digital filters to develop inverse filters for the loudspeaker/room response.
  • the invertability of these system responses has been studied and numerous solutions have been proposed.
  • Several of these solutions involve frequency domain transform techniques to design finite impulse response (“FIR”) filters.
  • FIR finite impulse response
  • one or more loudspeakers are located in a small to medium sized room such as a studio control room or domestic living room.
  • a test signal is output through a loudspeaker and received at a microphone, located near, but by necessity not coincident to, the location of the listener's ears.
  • Inverse filter coefficients are then generated from the measured transfer function. These coefficients are then transferred to a fixed digital filter for use in the playback mode, at which time the system processes the audio source material in real time.
  • Frequency response anomalies in a room are the results of the reinforcement and cancellation which occur when sound waves from various sources (i.e., direct and reflected) add together in and out of phase. It has been found that the average distance between pressure maxima in a room is about 0.9 times the
  • the auditory system has the ability to discriminate direct sound from later reflections, as well as the ability to detect the direction from which a sound is coming. It also perceives tones on a logarithmic frequency scale, rather than the linear range in which adaptive filters operate. While the ability to generate very accurate equalization filters is one of the goals of the known adaptive systems, i.e., minimize an error in the least mean squared sense, it is not necessarily correct from psychoacoustic criteria.
  • the filter coefficients an to a N-1 are updated based on an error signal e(n), which is the difference between the filter's output y(n) and a reference signal d(n).
  • Any known method may be used for performing this update including those described in "Adaptive Signal Processing", edited by L.H. Sibul, 1987 IEEE Press, New York. Such known methods typically attempt to minimize some function of the error signal e(n).
  • this technique can be used to adaptively design digital filters with responses matched to the given signals.
  • Figure 2 illustrates a predictive filter structure used for equalization, which is described in U.S. Patent No. 4,458,362 issued to Berkovitz et al.
  • the filter A(n) is updated based on the error between the current input signal sample and its predicted value y(n). If x(n) is the output of a system driven by a "white" sequence, it can be shown that the resulting filter is an inverse of the system response, with properties suitable for use as an equalizer.
  • a digital filter's frequency resolution is directly proportional to its length. If we define resolution to be the minimum 3 dB feature bandwidth, and assume that an adapted FIR filter represents a rectangularly
  • f res 0.89 x f s /N where f res is the resolution in Hertz, f s is the
  • N is the total number of FIR filter coefficients.
  • a common sampling frequency is 44,100 H z .
  • N For the filter to have better than 20 H z resolution, which would be needed for satisfactory equalization at low frequencies, N must be greater than 1960.
  • N In typical audio
  • An additional object of this invention is to provide a method for accurately adapting an FIR filter when a large number of filter taps are required to obtain adequate frequency resolution.
  • Yet another object of this invention is to provide an efficient means for implementing long FIR filters which do not introduce amplitude or phase distortions into the response by band splitting and recombination.
  • the system and method of the present invention provides a means for designing a single fixed FIR filter adaptively from measured data, in a manner whereby the filter's frequency and time resolution can be
  • the resulting filter exhibits properties which allow it to be efficiently implemented in various multi-rate configurations.
  • the system and method of the present invention exploits several properties of FIR filters to solve the problems associated with prior art systems.
  • the system and method produce an FIR filter with high resolution at low frequencies by having a large number of coefficients, but reduces resolution at higher frequencies by allowing only a fraction of the
  • coefficients to adapt to the high frequency part of the signal This is accomplished by using a multi-rate, segmented adaptation procedure, such that resolution and bandwidth are controlled independently at each stage. If desired, the resulting filter can be made to
  • Fig. 1 is a schematic view of an adaptive FIR filter.
  • Fig. 2 is a schematic view of a linear predictor equalizer.
  • Fig. 3(a)-3(d) are graphs of time domain and corresponding frequency domain results from operation of the method of the present invention.
  • Fig. 4 is a schmatic diagram showing the steps in the removal of the sampling artifacts from data.
  • Fig. 5 is a schmatic diagram of an adaptive FIR filter of the present invention.
  • Fig. 6 is an impulse response of an equalization filter using the system and method of the present invention.
  • Fig. 7 is a parallel implementation of the filter of the present invention.
  • Fig. 8 is a two stage multi rate implementation of the filter of the present invention.
  • Fig. 9 is a schmatic diagram of a three stage multi rate implementation of the filter of the present
  • Fig. 10 is a graph of the band-limited loudspeaker/ room response for which equalization is to be adapted using the system and method of the present invention.
  • Fig. 11 is a graph showing the impulse response of a 320 coefficient Equalization filter adapted using a conventional LMS approach.
  • Fig. 12 is a graph showing frequency response of the filter whose time response is shown in Fig. 11.
  • Fig. 13 is a graph of the impulse response of a 320 coefficient Equalization filter using the system and method of the present invention.
  • Fig. 14 is a graph of the frequency response of the filter whose time response is shown in Fig. 13.
  • Fig. 15 is a flow chart for the method of the present invention performing half band processing.
  • Fig. 16 is a schmatic diagram of the components of the present invention.
  • the basic principle set forth in the description that follows is the segmentation of an adaptive filter in both the time and frequency domains for the purpose of controlling the resolution of the resulting filter. This is accomplished by sequentially adapting portions of the final filter to data at different sampling rates, and using interpolation techniques to make the
  • a ROM or RAM 52 is used for storing test signals and is down loaded., from a host computer (not shown).
  • a signal RAM 56 is used for storing signals during processing and a suitable RAM would be the Motorola MCM 6164.
  • a clock 58 operates at a frequency which is a multiple of the desired system sampling frequencies and a program divider 60 generates various sampling frequencies from the clock 58.
  • a digital signal processing microcomputer 62 controls the operation of the system of the present invention by executing various signal processing
  • Example of a suitable digital signal processor is the Motorola DSP 56001. Secondary digital signal processors 64 operate in parallel to provide the necessary
  • a Sigma-Delta type analog digital converter 66 operates at various sampling frequencies and an antiliasing filter and sample and hold circuit are an inherent part of the Sigma-Delta design and a suitable device can be obtained from
  • a digital to analog conversion system 68 includes a digital
  • a Bessel type low pass filter 70 is used to remove the high frequency components from the output signal.
  • An optional interface 54 to the host computer 62 may also be used.
  • the system and method operate as follows. Given that the equalization filter is to operate over a total bandwidth of ⁇ Hz, then the sampling rate, f samp' is chosen such that f samp ⁇ 2 ⁇ in accordance with the well known Nyquist criterion for sampled signals.
  • the total filter length N is
  • the filter is then constructed from a set of adaptively- derived segments, such that the frequency resolution varies as a function of frequency.
  • segment is used here instead of "band” to differentiate the method of the present invention from that of
  • the filter may then be implemented in a conventional FIR filter structure, or in a preferred embodiment, as a parallel structure which exploits the special time-frequency relationship inherent in the coefficients, as discussed below and shown in Figure 7.
  • the table below illustrates the relationships between the various parameter of adaptation for the most general case.
  • the segment i is defined in terms of frequency range and resolution, and those parameters determine minimum values for the segment adaptation length p i , total length n i , and the sampling frequency f isamp .
  • the segment adaptation length p i is determined as follows:
  • n 0 coefficients of the first segment are set to zero, as shown in Figure 3a.
  • n 0 is equal to p 0 in the first segment adapted.
  • the coefficients are adapted according to any chosen adaptive algorithm, operating on input data sampled at the appropriate sample rate fosamp ' Tne resulting nn coefficients, shown in Figure 3b, comprise the first segment.
  • the filter is then interpolated by a factor L to length n 1 and scaled, forming the n 1 total filter coefficients at that stage, comprising the p 1 coefficients to be
  • the second segment consists of the first p 1 values readapted according to the chosen algorithm, this time with input data obtained at L times the
  • the Analog to Digital converter oversample the data by a factor of two, the resulting digitized samples processed through a half band filter and decimated by a factor of 2, with the output used by the adaptive filter. This is shown schematically in Figure 4. If the adaptation procedure is being performed in non-real time using previously sampled and stored data, then the data may be sampled at the higher rate and post processed in a similar manner to obtain equivalent results.
  • the length of the sampled data sequences which are processed by the filter during adaptation must be sufficient to allow the filter to converge for the given filter length chosen adaptation algorithm.
  • the convergence factor K is initially chosen to be near its maximum allowable value for stable behavior, a value which can be calculated from the total energy in the signal and the number of adapting coefficients in the filter using well-known relationships. Then, in order to minimize misadjustment, K is scaled by a constant less than but very close to 1.0 after each sampling interval. When the value of K becomes small enough that adaptation of the coefficients essentially ceases, then the process may be terminated, and the adapted filter coefficients used as the results of the current segment.
  • the adaptation is performed in non-real time using stored samples, a significant savings in memory may be achieved if a minimum data set is initially sampled and stored, then cycled through repeatedly while the convergence constant is reduced as described above.
  • the data sample size should be at least twice the total filter length n i of the segment being adapted.
  • test signal When the filter is used in the embodiment of an equalizer, the test signal must be chosen carefully so that a correct inverse filter can be generated.
  • the test signal must have a white spectrum and be uncorrelated, and in particular, this property should be ensured in a finite number of samples.
  • This can be achieved by using a maximum length sequence, or preferably obtained by creating a sequence with the desired properties using an inverse Fourier Transform method.
  • the magnitude of the frequency transform will be specified, and the phase component of the transform will be generated from a sequence of random numbers between + ⁇ and - ⁇ .
  • the real part of the transform is made symmetric about 0, and the imaginary part anti-symmetric.
  • an inverse transform to this data, such as is available using well known Fast Fourier Transform techniques, a time domain signal which is a power of 2 in length and has the desired spectral properties will be generated.
  • a further advantage of using such a method is its ability to generate any arbitrary spectral shape, which can be used to
  • test signal noise to have the inverse characteristic other than white, specifically that of the desired post equalization spectrum.
  • sample-by-sample adaptive algorithms such as the LMS never actually achieve the optimal solution for the coefficients at any given sampling interval, but rather do so only in the mean, performance may be improved by obtaining the mean using the following processing steps.
  • R additional samples are processed with a value of K several times greater than its final previous value.
  • the filter coefficients are copied from the adaptive filter and added into a suitable external memory array for the purposes of averaging.
  • the coefficient sums in the memory array are each divided by R to obtain their average value, and these are then used as the coefficient results of the current segment.
  • filter coefficients are obtained from the adaptation of the current segment, they must be further processed in order to be used as initial conditions for the next segment of the filter.
  • L 2 (half- band case) as noted earlier.
  • the lowpass interpolation filter may be designed using any of the well-known techniques for designing FIR filters. A particularly straightforward method is that of the window-function technique, described in most texts on digital filter design. For this application, the length of the
  • interpolating filter M must be odd and the quantity (M- 1)/(2L) an integer in order for the interpolation filter delay to be removed.
  • M interpolation filter delay
  • Interpolation of the segment filter coefficients is accomplished by inserting (L-1) zero value coefficients between each of the original coefficients, and appending [(M-1J/2] - 1 zeroes to the end, then convolving the resulting Ln i + [(M-1)/2]-1 coefficients with the M lowpass filter coefficients.
  • the resulting filter coefficients represent a filter which has the identical frequency response of the original filter in the lower 1/L part of its band, and a low pass characteristic above.
  • the interpolated and scaled filter coefficients are then used as the initial condition for the next stage of adaptation. It is at this step that restrictions are imposed on the filter in order to control resolution. For the case of segment 1, by constraining the filter to adapt only the first pi coefficients, and keeping the remaining [n 1 - p 1 ] coefficients constant at the
  • the adaptation process essentially converts the lowpass characteristic of the initial filter
  • FIG. 6 is an example of a filter adapted in the manner described above.
  • the desired high frequency resolution is rather broad, and can be obtained with a relatively short filter.
  • a longer filter is required, but since the additional
  • approximately half of the filter coefficients can be associated exclusively with the first segment.
  • the filter can be decomposed into a bank of parallel filters, each of which is related to a segment of the original filter.
  • S j are the p j coefficients adapted during segment j
  • S j - 1 are the remaining (p j -1 - n j ) adapted during segment j-1, and so on. Due to the manner in which each segment has been adapted and the structure of this implementation, each branch is band limited and delayed relative to the branch above it in the diagram. It is therefore possible to implement each branch at a
  • resulting filter response are necessarily introduced due to the fact that the delay and phase shift introduced by the decimation and interpolation process cannot be removed and are not related in any way to the filter response being implemented.
  • Figure 8 shows a two stage multi-rate
  • Figure 9 shows a three-stage implementation. As will be obvious to those skilled in the art, further extensions to greater than three stages may be desirable as a means of further reducing the computational load in real time applications and can be accomplished by extension of this technique.
  • FIG. 10 shows the response to be equalized
  • Figures 11 and 12 show the filter impulse and frequency response, respectively, for a 320 coefficient filter using conventional (i.e. single step) LMS adaptation.
  • the filter has a
  • Figure 13 and 14 show the results of a 4 segment
  • segment is # adaptive taps resolution freg. range

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  • Filters That Use Time-Delay Elements (AREA)

Abstract

Un filtre adaptif comprend une mémoire (52) destinée à stocker des signaux de test et est transféré d'un ordinateur central par l'intermédiaire d'un dispositif facultatif assurant l'interface (54). Une mémoire (56) est utilisée pour stocker des signaux pendant le traitement. Une horloge (58) fonctionne à une fréquence qui est un multiple des fréquences d'échantillonnage du système voulu. Un diviseur de programme (60) génère diverses fréquences d'échantillonnage à partir de l'horloge (58). Un processeur (62) de signaux numériques commande le fonctionnement du système. Des processeurs (64) de signaux numériques secondaires fonctionnent en parallèle afin de fournir la puissance de calcul nécessaire. Un convertisseur analogique/numérique (66) de type sigma/delta fonctionnant à diverses fréquences d'échantillonnage est connecté à l'entrée du processeur (62). Un convertisseur numérique/analogique (68) comprenant un filtre d'interpolation est connecté à la sortie du processeur (62). Un filtre passe-bas (70) de type Bessel est utilisé afin d'éliminer les composantes de haute fréquence du signal de sortie.
PCT/US1991/006846 1990-09-21 1991-09-20 Systeme et procede de production d'un filtre numerique a reponse impulsionnelle finie adaptatif a resolution de frequence non lineaire WO1992005501A1 (fr)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113015052A (zh) * 2019-12-20 2021-06-22 Gn 奥迪欧有限公司 低频噪声降低的可穿戴电子设备

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4349889A (en) * 1979-07-18 1982-09-14 U.S. Philips Corporation Non-recursive filter having adjustable step-size for each iteration
US4458362A (en) * 1982-05-13 1984-07-03 Teledyne Industries, Inc. Automatic time domain equalization of audio signals
US4628530A (en) * 1983-02-23 1986-12-09 U. S. Philips Corporation Automatic equalizing system with DFT and FFT
US4872184A (en) * 1987-07-21 1989-10-03 Nec Corporation Digital automatic line equalizer with means for controlling tap gains of transversal filter based on mean power of output from the filter
US4995030A (en) * 1988-02-01 1991-02-19 Memotec Datacom, Inc. Far end echo cancellation method and apparatus
US5058047A (en) * 1989-05-30 1991-10-15 Advanced Micro Devices, Inc. System and method for providing digital filter coefficients

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4349889A (en) * 1979-07-18 1982-09-14 U.S. Philips Corporation Non-recursive filter having adjustable step-size for each iteration
US4458362A (en) * 1982-05-13 1984-07-03 Teledyne Industries, Inc. Automatic time domain equalization of audio signals
US4628530A (en) * 1983-02-23 1986-12-09 U. S. Philips Corporation Automatic equalizing system with DFT and FFT
US4872184A (en) * 1987-07-21 1989-10-03 Nec Corporation Digital automatic line equalizer with means for controlling tap gains of transversal filter based on mean power of output from the filter
US4995030A (en) * 1988-02-01 1991-02-19 Memotec Datacom, Inc. Far end echo cancellation method and apparatus
US5058047A (en) * 1989-05-30 1991-10-15 Advanced Micro Devices, Inc. System and method for providing digital filter coefficients

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113015052A (zh) * 2019-12-20 2021-06-22 Gn 奥迪欧有限公司 低频噪声降低的可穿戴电子设备

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