(19) United States
`(12) Patent Application Publication (10) Pub. No.: US 2004/0071284 A1
`(43) Pub. Date:
`Apr. 15, 2004
`Abutalebi et al.
`
`US 20040071284A1
`
`(54) METHOD AND SYSTEM FOR PROCESSING
`SUBBAND SIGNALS USINGADAPTIVE
`FILTERS
`
`(76) Inventors: Hamid Reza Abutalebi, Yazd (IR);
`Robert L. Brennan, Kitchener (CA);
`Hamid Sheikhzadeh-Nadjar, Waterloo
`(CA); Dequn Sun, Neuchatel (CH)
`Correspondence Address:
`PERMAN & GREEN
`425 POST ROAD
`FAIRFIELD, CT 06824 (US)
`Appl. No.:
`10/642,847
`Aug. 18, 2003
`Foreign Application Priority Data
`
`(21)
`(22)
`(30)
`
`Filed:
`
`Aug. 16, 2002 (CA).......................................... 2,399,159
`
`Publication Classification
`
`(51) Int. Cl." ...................................................... H04M 9/08
`(52) U.S. Cl. ................................. 379/406.08: 379/406.14
`(57)
`ABSTRACT
`A method and System for processing Subband Signals using
`adaptive filters is provided. The System is implemented on
`an oversampled WOLA filterbank. Inputs signals are over
`Sampled. The System includes an adaptive filter for each
`Subband, and the functionality of improving the conver
`gence properties of the adaptive filter. For example, the
`convergence property is improved by whitening the Spectra
`of the oversampled Subband Signals and/or affine projection
`algorithm. The System is applicable to echo and/or noise
`cancellation. Adaptive Step size control, adaptation process
`control using Double-Talk detector may be implemented.
`The System may further implement a non-adaptive proceSS
`ing for reducing uncorrelated noise and/or cross-talk resis
`tant adaptive noise cancellation.
`
`16
`WOLA
`Analysis -
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`Page 1
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`IPR PETITION
`US RE48,371
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`US 2004/0071284 A1
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`Apr. 15, 2004
`
`METHOD AND SYSTEM FOR PROCESSING
`SUBBAND SIGNALS USINGADAPTIVE FILTERS
`
`BACKGROUND OF THE INVENTION
`0001) 1. Field of the Invention
`0002 The present invention relates to signal processing,
`more Specifically to a method and System for processing
`Subband Signals using adaptive filters.
`0003 2. Background
`0004.
`It is well known that a noise cancellation system
`can be implemented with a fullband adaptive filter working
`on the entire frequency band of interest. The Least Mean
`Square (LMS) algorithm and its variants are often used to
`adapt the fullband filter with relatively low computation
`complexity and adequate performance when the interfering
`signal is white. However, the fullband LMS solution Suffers
`from Significantly degraded performance with colored inter
`fering Signals due to large eigenvalue spread and slow
`convergence. Moreover, as the length of the LMS filter is
`increased, the convergence rate of the LMS algorithm
`decreases and computational requirements increase. This is
`problematic in applications, Such as acoustic echo cancel
`lation, which demand long adaptive filters to model the
`return path response and delay. These issues are especially
`important in portable applications, where processing power
`must be conserved.
`0005. As a result, Subband adaptive filters (SAFs)
`become an interesting and viable option for many adaptive
`systems. The SAF approach uses a filterbank to split the
`fullband Signal input into a number of frequency bands, each
`Serving as input to an adaptive filter. This Subband decom
`position greatly reduces the update rate and the length of the
`adaptive filters resulting in much lower computational com
`plexity.
`0.006) Subband signals are often maximally decimated in
`SAF systems by critical Sampling. This leads to a whitening
`of the input Signals and an improved convergence behavior.
`For example, there is an SAF System with critical Sampling
`(A. Gilloire and M. Vetterli," Adaptive Filtering in Subbands
`with Critical Sampling: Analysis, Experiments and Appli
`cations to Acoustic Echo Cancellation”. IEEE Trans. Signal
`Processing, vol. SP-40, no. 8, pp. 1862-1875, August 1992).
`0007. However, the maximal decimation/critical Sam
`pling creates aliasing problems. The presence of aliasing
`distortion requires the use of adaptive croSS-filters between
`adjacent Subbands or gap filterbanks. Systems with croSS
`filters generally converge slower and have higher computa
`tional cost, while gap filterbanks produce Significant Signal
`distortion.
`0008. It is therefore desirable to provide a method and
`System for processing Subband Signals using adaptive filters,
`facilitating high Speed processing, low power consumption
`and high quality.
`
`SUMMARY OF THE INVENTION
`0009. It is an object of the present invention to provide a
`method and System which obviates or mitigates at least one
`of the disadvantages described above.
`0010. In accordance with an aspect of the present inven
`tion, there is provided a method of processing Subband
`
`Signals for cancelling an undesired effect on a signal, the
`method comprising Steps of: analysing a primary Signal,
`which has a signal affected by an undesired signal, and a
`reference Signal corresponding, to the undesired Signal to
`produce frequency domain primary Signals and frequency
`domain reference signals in a plurality of Subbands, pro
`cessing the frequency domain primary Signal and the fre
`quency domain reference Signal using an adaptive filter in
`each Subband, comprising operating on at least the fre
`quency domain reference Signal to improve the convergence
`of the adaptive filter in each Subband; and Synthesizing the
`outputs of the adaptive processing blocks to output a time
`domain Signal in which the effect of the reference has been
`cancelled.
`0011. In accordance with a further aspect of the present
`invention, there is provided a System for processing Subband
`Signals for cancelling an undesired effect on a signal. The
`System includes: an analysis filterbank for analysing a
`primary Signal, which has a signal affected by an undesired
`Signal, and a reference Signal corresponding, to the undes
`ired signal to produce frequency domain primary Signals and
`frequency domain reference Signals in a plurality of Sub
`bands, a processing module for processing the frequency
`domain primary Signals and the frequency domain reference
`Signals, including an adaptive filter module in each Subband,
`and a module for operating on at least the frequency domain
`reference Signal to improve the convergence of each adap
`tive filter, and a Synthesis filterbank for Synthesizing the
`outputs of the processing module to output a time domain
`Signal in which the effect of the reference has been can
`celled.
`0012. A further understanding of other features, aspects
`and advantages of the present invention will be realized by
`reference to the following description, appended claims, and
`accompanying drawings.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`0013 The invention will be further understood from the
`following description with reference to the drawings in
`which:
`0014 FIG. 1 is a block diagram showing a Subband
`adaptive filter (SAF) system in accordance with a first
`embodiment of the invention;
`0015 FIG. 2 is a block diagram showing an SAF system
`in accordance with a Second embodiment of the invention;
`0016 FIG. 3 is a block diagram showing an SAF system
`in accordance with a third embodiment of the invention;
`0017 FIGS. 4A-4C are graphs showing signal spectra of
`FIG. 3;
`0018 FIG. 5 is a block diagram showing a SAF system
`in accordance with a fourth embodiment of the invention;
`0019 FIG. 6 is a graph showing an average normalized
`filter MSE (measured mean-squared error) for speech in 0
`dB SNR White noise for no whitening, whitening by spectral
`emphasis, and whitening by decimation;
`0020 FIG. 7 is a graph showing eigenvalues of the
`autocorrelation matrix of the reference signal for no whit
`ening, whitening by Spectral emphasis, whitening by deci
`mation, and whitening by decimation and spectral emphasis,
`
`Page 24
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`
`0021 FIG. 8 is a graph showing MSE error for no
`whitening, whitening by Spectral emphasis, whitening by
`decimation, and whitening decimation and Spectral empha
`Sis,
`0022 FIG. 9 is a graph showing MSE error for Affine
`Projection Algorithm (APA) with different orders;
`0023 FIG. 10 is a block diagram showing an application
`of adaptive Systems for echo cancellation;
`0024 FIG. 11 is a block diagram showing an over
`Sampled SAF system for echo cancellation in accordance
`with a first embodiment of the present invention;
`0.025
`FIG. 12 is a block diagram showing a first embodi
`ment of an adaptive processing block (APB) of FIG. 11;
`0.026
`FIG. 13 is a block diagram showing a second
`embodiment of the APB of FIG. 11;
`0.027
`FIG. 14 is a block diagram showing a third
`embodiment of the APB of FIG. 11;
`0028 FIG. 15 is a block diagram showing a fourth
`embodiment of the APB of FIG. 11;
`0029 FIG. 16 is a graph showing the coherence function
`of diffuse noise;
`0030 FIG. 17 is a block diagram showing an over
`Sampled SAF system in accordance with a Second embodi
`ment of the invention;
`0.031
`FIG. 18 is a block diagram showing one embodi
`ment of an adaptive processing block (APB) and a non
`adaptive processing block (NAPB) of FIG. 17;
`0.032
`FIG. 19 is a block diagram showing a cross-talk
`resistant APB in accordance with an embodiment of the
`present invention;
`0.033 FIG.20 is a diagram showing an oversampled SAF
`System in accordance with a third embodiment of the present
`invention;
`0034 FIG.21 is a diagram showing an oversampled SAF
`System in accordance with a fourth embodiment of the
`present invention; and
`0.035
`FIG. 22 is a diagram showing an example of the
`Subband processing block of FIG. 21.
`
`DETAILED DESCRIPTION OF THE
`PREFERRED EMBODIMENT(S)
`0036) Subband adaptive filter (SAF) systems in accor
`dance with embodiments of the present invention are illus
`trated in FIGS. 1-3. The SAF systems 10A-10C of FIGS. 1-3
`have the functionality of improving the convergence prop
`erties of adaptive filters. The SAF system is implemented
`using an oversampled weighted overlap-added (WOLA)
`filterbank. The oversampled WOLA filterbanks are
`described in U.S. Pat. No. 6,236,731, U.S. Pat. No. 6,240,
`192, and R. Brennan and T. Schneider, "A Flexible Filter
`bank Structure for Extensive Signal Manipulations in Digital
`Hearing Aids”, Proc. IEEE Int. Symp. Circuits and Systems,
`pp.569-572, 1998, which are incorporated by reference. The
`oversampled WOLA filterbank may be implemented using a
`digital signal processor (DSP) technology.
`
`pre
`
`0037. The oversampled WOLA filterbank has a WOLA
`analysis filterbank for transforming input signals into over
`Sampled Subband Signals, Subband Signal processors for
`processing overSampled Subband Signals using adaptive
`filters and a WOLA synthesis filterbank for combining the
`Subband Signals. The Spectra of the oversampled Subband
`Signals are not white. When OverSampling factors of 2 and
`4 are employed for example, their spectral bandwidth is
`limited to J/2 and JL/4 respectively. A critically Sampled
`System by comparison produces Subband Signals in the
`complete range from dc to J.L. In the SAF systems 10A-10C
`described below, the oversampled Subband Signals are whit
`ened to increase the convergence rate of the adaptive filters.
`The inherent benefit of decreased spectral dynamics result
`ing from Subband decomposition is, therefore, not lost due
`to oversampling.
`0038. The SAF system 10A of FIG. 1 is now described
`in detail. The SAF system 10A has the functionality of
`whitening oversampled Subband Signals in their spectra by
`Spectral emphasis, which increases the convergence rate of
`the Least Mean-Square (LMS) algorithm. In SAF system
`10A, an unknown plant P(z) 12 is modeled by an adaptive
`filter W(z) 14.
`0039. The SAF system 10A includes WOLA analysis
`filterbanks 16 and 18 and a plurality of Subband processing
`blocks. In FIG. 1, a Subband processing block 5A for
`Subband i is illustrated. This block includes emphasis filters
`ge(z) 20 and 22, an LMS block 24, a secondary adaptive
`filter W(z) 26, and an adder 28. The Subband processing
`block 5A may be employed for each Subband.
`0040. The WOLA analysis filterbank 16 receives a ref
`erence signal x(n). The WOLA analysis filterbank 18
`receives a primary signal d(n) via the plant P(Z) 12. The
`WOLA analysis filterbanks 16 and 18 convert their input
`Signals into a plurality of oversampled Subband Signals.
`0041. During WOLA analysis, the Subband signals are
`decimated by a factor of M/OS, where M is the number of
`filters, and OS is the oversampling factor. At this stage, the
`Subband Signals are no longer full-band. At the output of the
`WOLA analysis filterbanks 16 and 18, i.e., points 1 and 2 of
`FIG. 1, their bandwidth is L/OS. Thus the spectra are
`colored but in a predictable, constant manner. The emphasis
`filters g(z) 20 and 22 then amplify the high frequency
`contents of the Signals at the points 1 and 2, respectively, to
`obtain almost white Spectra. The input to the Secondary
`adaptive filter W(z) 26, i.e., a signal at point 3, is whitened
`by the output of the emphasis filter g(z) 20.
`0042. The adder 28 adds the output of the emphasis filter
`g(z) 22 and the output of the secondary adaptive filter
`W(z) 26. The LMS block 24 receives the output of the
`emphasis filter g(z) 20 and the output of an adder 28, and
`adjusts the filter coefficients of the secondary adaptive filter
`W(z) 26. The LMS block 24 may implement any of the
`common variants of the LMS algorithm. Typically the leaky
`normalized LMS algorithm is used for its stability and low
`computational cost. In each Subband, the coefficients of the
`adaptive filter W(z) 26 are copied to the adaptive filter
`W(z) 14. In each Subband, the adaptive filter W(z) takes, as
`its input, the non-emphasized version of the Subband Signal
`at the point 1.
`
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`0043. The SAF system 10A further includes an adder 30
`which receives the output from the adaptive filter W(z) 14
`and the Signal at the point 2, and outputs a Subband Signal
`
`0044) The signals e(n) (i=0, 1,..., K-1) are combined
`in a synthesis filterbank (not shown) of the oversampled
`WOLA filterbank. In this case, the synthesis filterbank
`processes signals that are not affected by the emphasis filters
`g(z) 22 and 24.
`0045. The design of the emphasis filters g(z) 22 and 24
`is dependent on the OverSampling factor OS used in the
`WOLA filterbank. The filter gain (G) of the emphasis filters
`g(z) 20 and 22 is a design parameter that depends on the
`WOLA analysis filter shape. Given the oversampled WOLA
`filterbank parameters, the spectral properties of the Subband
`Signals are determined, and an appropriate emphasis filter is
`designed. The filters may be implemented as a Finite
`Impulse Response (FIR) filter, an Infinite Impulse Response
`(IIR) filter, or any other filter type.
`0046. In the case of two times oversampling, the bottom
`half of the Subband Spectrum has relatively high energy and
`is relatively flat compared to the upper half of the Spectrum,
`which contains very little energy. In this case, the emphasis
`filter g(z) amplifies the high-frequency portion of the
`Spectrum. The filtering operation, thus, results in a signal
`Spectrum that is whitened.
`0047 Alternatively, high-pass noise may be added to the
`bandpass signals to whiten them as described in FIG. 2. The
`SAF system 10B of FIG. 2 is now described in detail. The
`SAF system 10B includes the functionality of whitening by
`additive noise.
`0048. The reference signal X(n) and the primary signal
`d(n) are processed at the WOLA analysis filterbanks 16 and
`18 as described above. The SAF system 10B includes a
`Subband processing block. In FIG. 2, the Subband process
`ing block 5B for Subband i is illustrated. The Subband
`processing block 5B includes adders 28 and 32, an estima
`tion block 36 for estimating the average power G of the
`Signal at the point 1, a mixing block 38 for mixing the
`average power G and a signal an) from a high-pass noise
`Source, the LMS block 24 and a secondary adaptive filter
`W(z) 40. The average power G of the signal at the point 1
`is used to modulate the high-pass noise a(n). The adder 32
`adds the signal at the point 1 and the output Ga(n) of the
`mixing block 38. The input to the secondary adaptive filter
`W(z) 40, i.e., a signal at the point 3, is whitened by adding
`G.a(n) to the Signal at point 1. The adder 28 adds the signal
`at the point 2 and the output of the Secondary adaptive filter
`W(z) 40. The LMS block 24 receives the outputs of the
`adders 32 and 34, and adjusts the filter coefficients of the
`secondary adaptive filter W(z) 40. The coefficients of the
`secondary adaptive filter W(z) 40 are copied to the adaptive
`filter W(z) 14. The adaptive filter W(z) 14 processes the
`Signal at the point 1, which is not processed by additive
`noise. The adder 30 receives the output from the adaptive
`filter W(z) 14 and the signal at the point 2, and outputs a
`Subband Signal e(n).
`0049. The SAF system 10C of FIG. 3 is now described
`in detail. The SAF system 10C includes the functionality of
`whitening by decimation.
`0050. The reference signal X(n) and the primary signal
`d(n) are processed at the WOLA analysis filterbanks 16 and
`
`18 as described above. The SAF system 10C includes a
`Subband processing block. In FIG. 3, the Subband process
`ing block 5C for Subband i is illustrated. The Subband
`processing block 5C includes decimation blocks 42 and 44,
`the LMS block 24, the adder 28, and a secondary adaptive
`filter W(z) 48. The Subband signals at the points 1 and 2
`derived from the reference input X(n) and the primary input
`d(n) are further decimated by a factor of DECC=OS at the
`blockS 42 and 44, respectively. Best performance is usually
`obtained by setting DEC to be less than OS. Assume,
`without loss of generality, that DEC is set to: DEC=OS-1.
`The input to the secondary adaptive filter W(z) 48, i.e., a
`Signal at the point 3, is whitened by decimating the Signal at
`the point 1. The adder 28 adds the output of the block 44 and
`the output of the secondary adaptive filter W(z) 48. The
`LMS block 24 receives the outputs of the blocks 42 and 44,
`and adjusts the filter coefficients of the Secondary adaptive
`filter W(z) 48. The filter coefficients of the secondary
`adaptive filter W(z) 48 are expanded at a block 50. The
`expanded filter coefficients at a point 4, i.e. the output of the
`block 50 are copied to the adaptive filter W(z) 14. The
`adaptive filter W(z) 14 processes the signal at the point 1,
`which is not processed at the blocks 42 and 50. The adder 30
`receives the output from the adaptive filter W(z) 14 and the
`Signal at the point 2, and outputs a Subband Signal e(n).
`0051 Whitening by decimation is most effective for
`oversampling factor OS's of more than 2, while whitening
`by Spectral emphasis or by adding noise is most effective for
`oversampling factor OS's of 2 or less.
`0052 FIG. 4A shows signal spectra at the points 1 and 2
`of FIG. 3. FIG. 4B shows signal spectra at the point 3 of
`FIG. 3. FIG. 4C shows signal spectra at the point 4 of FIG.
`3. As illustrated in FIG. 4B, decimating by a factor of DEC
`increases the bandwidth to c(OS-1)/OS (371/4 for OS=4)
`without generating in-band aliasing. Due to the increased
`bandwidth, the LMS algorithm at the LMS block 24 now
`converges much faster. To be able to use the adaptive filter
`W(z) 14, the filter parameter of the secondary adaptive filter
`W(z) is expanded by OS-1. This may create in-band
`images as shown in FIG. 4C. However, since the low-pass
`Signal at the point 1 does not contain Significant energy when
`()>TL/OS, these spectral images will not contribute to error.
`0053) The SAF systems 10A-10C implemented on the
`oversampled WOLAfilterbank (referred to as a oversampled
`SAF system) are applicable in a wide range of technology
`areas, including adaptive noise reduction, adaptive direc
`tional Signal processing with microphone arrays, feedback
`reduction for hearing aids, and acoustic echo cancellation.
`The logic contained in the Sub-band processing blockS
`5A-5C is dependent on a particular application.
`0054) One of either the reference signal x(n) or the
`primary Signal d(n) may be a digital signal corresponding to
`a speaker contaminated with interfering noise, and the other
`may be a digital Signal corresponding to the interfering
`noise. In this case, the OverSampled SAF System cancels
`noise in the transmitted Speech. The Subband processing
`blocks 5A-5C remove the contaminated portion from the
`desired signal by removing the correlated elements of the
`two signals by using the LMS algorithm. Since the over
`Sampled Subband Signals are now whitened in their spectra,
`the oversampled SAF system performs noise cancellation at
`high Speed enhancing the Signal experienced by the listener.
`
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`0055. The oversampled SAF system may be used for
`acoustic echo cancellation or acoustic feedback cancellation.
`In the case for the echo cancellation, one of either the
`reference Signal X(n) or the primary signal d(n) may be a
`digital signal that has a desired signal affected by an echo,
`while the other is a digital Signal corresponding to the echo.
`0056. The LMS parameters at the LMS block 24, such as
`LMS Step-Size, may vary in each Subband. For example,
`when lower Subbands contain speech content, the lower
`Subbands may have a Smaller Step-Size, while higher Sub
`bands may be more adapted with a larger Step-Size due to
`relatively low speech content. While the LMS technique is
`described above, other techniques Such as recursive least
`Squares may also be applicable.
`0057 Another method of improving the convergence rate
`is to employ adaptation Strategies that are fundamentally leSS
`Sensitive to eigenvalue Spread problem. One of these Strat
`egies is the adaptive algorithm called the affine projection
`algorithm (APA). The APA forms a link between Normal
`ized LMS (NLMS) and the Recursive Least Square (RLS)
`adaptation algorithms. The benefits of faster convergence of
`the RLS algorithm (it is expected to be largely insensitive to
`the eigenvalue spread problem) and the low computational
`requirements of the NLMS are combined in the APA. An
`SAF system with affine projection will now be described in
`detail.
`0058. In NLMS, the new adaptive filter weights best fit
`the last input vector to the corresponding desired signal. In
`APA, this fitting expands to the P-1 past input vectors (P
`being the APA order). Adaptation algorithm for the P" order
`APA can be summarized as follows:
`0059) 1) update X, and d.
`0060) 2) e=d,X, W,
`
`where:
`0063 X: an LXP matrix containing P past input
`VectOrS
`0064 d: a vector of the past P past desired signal
`Samples
`0065 W: adaptive filter weights vector at time in
`0066 C.: regularization factor
`0067 u: adaptation step size
`0068 The convergence of APA is surveyed in K. Ozeki
`and T. Umeda, “An adaptive algorithm filtering using an
`orthogonal projection to the affine Subspace and its proper
`ties,'Electronics and Communications in Japan, vol. 67-A,
`no. 5, pp. 19-27, Feb. 1984, and M. Montazeri and P.
`Duhamel, “A set of algorithms linking NLMS and block
`RLS algorithms’IEEE Tran. On Signal Processing, vol. 43,
`no. 2, pp. 444-453, Feb. 1995. As the projection order P
`increases, the convergence rate of APA becomes less depen
`dent on the eigenvalue Spread. Increasing the APA order
`results in faster convergence at the cost of more computa
`tional complexity of the adaptation algorithm.
`0069 FIG. 5 shows an SAF system 10D in accordance
`with a fourth embodiment of the present invention. The SAF
`system 10D includes the WOLA analysis filterbanks 16 and
`
`18, and a plurality of APA Subband processing blocks. In
`FIG. 5, a sub-band processing block 5D for Subband i is
`illustrated. The Sub-band processing block 5D contains an
`adaptive filter using APA to adapt its weights Wi(n) (n:
`time).
`0070 The SAF system 10D may be implemented on an
`oversampled WOLA filterbank. For computational simplic
`ity, an APA of order P=2 may be applied, producing faster
`convergence with minimal increase in complexity. In this
`case, the matrix X'X, is approximated by R (autocorrela
`tion matrix of the reference signal) as described in V.
`Myllyla, “Robust fast affine projection algorithm for acous
`tic echo cancellation,” in proc. of Inter. Workshop on Acous
`tic Echo and Noise Control, September 2001.
`0.071) For P=2, it is sufficient to estimate only the first two
`autocorrelation coefficients (r(0) and r(1)) and then invert
`the matrix R, analytically. A first order recursive Smoothing
`filter may be used to estimate r(0) and r(1).
`0072. It is possible to combine any two or more of the
`techniques described in FIGS. 1-3 and 5 to achieve higher
`performance. For example, whitening by decimation
`improves the convergence rate by increasing the effective
`bandwidth of the reference signal. Whitening by spectral
`emphasis improves the convergence as before by limiting
`the Stop band loss thereby increasing the Smallest eigenval
`CS.
`0073 FIG. 6 shows an average normalized filter MSE
`(mean-square error) for speech in 0 dB SNR White noise. In
`FIG. 6, (a) represents MSE without whitening, (b) repre
`Sents MSE for whitening by spectral emphasis, and (c)
`represents MSE for whitening by decimation. The SAF
`System is used for noise cancellation, in which the SAF
`System receives inputs from 2-microphone. In this case,
`whitening by decimation converges faster than the other two
`methods. Since the adaptive filter operates at low frequency,
`whitening by decimation requires less computation than
`whitening by Spectral emphasis or whitening by adding
`OSC.
`0074) Detailed mathematical models of SAF systems are
`described in S. Weiss, “On Adaptive Filtering in Over
`sampled Sub-bands”, PhD. Thesis, Signal Processing Divi
`Sion, University of Strathclyde, Glasgow, May 1998, and S.
`Weiss et al., “Polyphase Analysis of Subband Adaptive
`Filters",33' Asilomar Conference on Signals, Systems, and
`Computers, Monterey, Calif., 1999.
`0075 FIG. 7 shows the theoretical eigenvalues of the
`autocorrelation matrix of the reference Signal for: no whit
`ening, whitening by Spectral emphasis, whitening by deci
`mation; and whitening by decimation and Spectral emphasis.
`The eigenvalues are calculated using an analytical formula
`given by the following reference: Dennis R. Morgan, “Slow
`Asymptotic Convergence of LMS Acoustic Echo Cancel
`ers”, IEEE Trans. Speech and Audio Proc., Vol. 3, No. 2, pp.
`126-136, March 1995. Small eigenvalues lead to slow
`convergence. The improvement can be seen at a low index
`area. AS the result of the above technique, i.e., whitening by
`Spectral emphasis, whitening by decimation or the combi
`nation of these methods, the eigenvalues become larger than
`that of no-whitening.
`0076. In FIG. 7, while whitening by spectral emphasis
`and by decimation both offer improvement (demonstrated by
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`a rise in the eigenvalues), a combination of both methods is
`more promising. This conclusion is confirmed by the mean
`squared error (MSE) results shown in FIG.8. FIG. 8 shows
`MSE error for: no whitening; whitening by spectral empha
`sis, whitening by decimation; and whitening by decimation
`and spectral emphasis. FIG. 9 shows the MSE error for APA
`with orders of P=1, 2, 4 and 5. The APA for P=1 yields an
`NLMS system. As shown, increasing the AP order, improves
`both the convergence rate and the MSE.
`0.077
`Fast adaptation techniques for echo cancellation
`are now described in detail. In echo cancellation, the long
`filter lengths, which are required because of the long dura
`tion associated with each echo path, may result in Slow
`convergence. The fast adaptation techniques described
`below allow echo cancellation Systems, which use long filter
`lengths, to cancel echo at high Speed. The fast adaptation
`techniques may also be applicable to other applications,
`Such as noise cancellation.
`0078 FIG. 10 shows an application of adaptive systems
`for echo cancellation. A Far-End (FE) acoustic input signal
`102 is converted to an electrical signal x(t) at a FE micro
`phone (MIC) 104, which is sent to a Near-End (NE) speaker
`106. The NE microphone (MIC) 110 then receives an
`acoustic echo signal 108 (referred to as FE echo) from the
`NE speaker 106. The NE microphone 110 also receives NE
`input signal 112 (e.g., speech and noise), and converts the
`total signal (=FE echo 108+NE input 112) to an electric
`Signal d(t). The electrical Signal x(t) is provided to an
`adaptive filter 118. The adder 114 adds the electrical signal
`d(t) and the output of the adaptive filter 118 for producing an
`error signal e(t). The adaptive filer 118 minimizes the error
`signal e(t) to eliminate the FE echo 108. Once convergence
`has been achieved, the adaptive filter 118 essentially models
`the transfer function of the NE speaker 106 and NE micro
`phone 110, as well as the transfer function of the acoustic
`path between the NE speaker 106 and the NE