RTL607_1027-0001
`
`Realtek 607 Ex. 1027
`
`

`
`speech signal is also distorted by the addition of rever-
`beration. Reduction of the SNR in dB is approxi-
`mated as l0 log“, L [6], where L is the number of
`microphones used.
`The second method uses a channel switching tech-
`nique, as shown in Fig. 2. Assuming that each near-
`end person is assigned a microphone and only one
`person talks at a time, the channel switching unit ac-
`tuates one of the L microphones corresponding to this
`near-end talker. In the receiving mode, this micro-
`phone is still actuated (since it is more likely for this
`person to talk again) and the AEC is updated to track
`this echo path and reduce the acoustic echo. Channel
`switching occurs only when the near-end talker
`changes. Because only one channel is updated for this
`multiple channel system, performance suffers when
`the microphone switches and the recovery is delayed
`until the convergence of the filter is achieved.
`The third method uses a memory bank to assist the
`channel switching method as shown in Fig. 3 [7,8].
`The transfer functions of the acoustic echo paths are
`estimated for each microphone off'—line, and the opti-
`mum echo canceller filter coefficients are stored in
`
`memory. In receive mode, only one of the L micro-
`phones is actuated (called the ON-MIC). The corre-
`sponding filter coefficients are loaded into acoustic
`echo canceller and AEC is updated to perform echo
`cancellation task. When channel switching occurs in
`the subsequent receiving mode, these updated filter
`coefficients are restored into the memory and the
`filter coefficients corresponding to the current ON-
`MIC will be loaded into AEC and updated.
`However, this method still has difficulties in real-
`time implementation due to the following two rea-
`sons. First, it requires a large memory to store all the
`filter coefficients. Since the impulse response of
`acoustic echo path has very long tails, the order of the
`echo canceller has to be large for a desired amount of
`echo cancellation. For example, for a 40-dB echo can-
`
`Microphone
`selection
`and gain
`control unil
`
`RXIH
`
`term of Eq. { 3 ) shows that excess mean square error is
`increased when a large N is used, and the third term
`shows the numerical error (due to coefficient quanti-
`zation and roundoff) is increased with a large N at a
`small _u. Furthermore, in a fixed-point processor, the
`problem of roundoff causes early termination of the
`adaptation of the coefficients when a small it is used
`[3]. In order to alleviate these problems, a higher dy-
`namic range can be achieved by using floating—point
`arithmetic, with the added cost of a more expensive
`hardware implementation [4 ] .
`A multiple-microphone acoustical echo cancella-
`tion system is shown in Fig. 2. In this figure, the near-
`end conference room consists of a loudspeaker and an
`array of microphones. Because it is a full duplex sys-
`tem, the transmit signal (sent out} contains the de-
`sired speech from the near-end talker, ambient noise,
`and the acoustic echo. The acoustic echo canceller is
`
`employed in the system to remove the unwanted echo.
`Since more than one microphone is used in the confer-
`ence room, we encounter a problem of multiple echo
`paths from the loudspeaker to each microphone.
`Three techniques are developed to accommodate
`multiple microphones into the acoustic echo cancella-
`tion system. The first technique simply mixes the
`output of all microphones [5]. This method has its
`major drawback of reducing signal—to—noise ratio
`(SNR) by adding up the ambient room noise, and the
`
`Conference Room
`
`M I
`
`M
`
`mixing}
`switching
`
`mb
`
`o o (
`
`3/
`
`’
`
`loud speaker
`
`ICCCWC in
`
`loud speaker
`
`|'0CCi\'¢ in
`
`FIG. 2. Block diagram of multirnicrophone AEC system.
`
`FIG. 3. Switching technique.
`
`Echo Paths
`
`RTL607_1027-0002
`RTL607_1027—0002
`
`

`
`cellation in a medium sized room with 0.5 sec. rever-
`
`beration time, an FIR filter of order over 3000 is re-
`quired. Assuming that eight microphones are used in
`a conference room, the total memory required to store
`all the filter coefficients is 24,000 words (each word
`may be 16-bit or 32-bit if floating-point arithmetic is
`used). Second, this method can only work in the
`static environment where the transfer functions from
`
`the loudspeaker to every microphones are assumed to
`be time-invariant. This assumption is not true in gen-
`eral, since the room environment changes from time
`to time. Hence the stored filter coeflicients are not
`
`always optimal for echo cancellation. As a result, this
`technique still sufl'ers from the abrupt decreasing in
`performance at the instance of channel switching as
`well as large memory requirement.
`
`3. THE PARTIAL ADAPTIVE PROCESS
`
`In this section, a technique called the partial adap-
`tive process is developed. This process is proposed to
`solve the difliculties (memory requirement and time-
`varying environment criteria) encountered in the
`switching technique. The partial adaptive process is
`shown in Fig. 4. In this figure, the far-end speech :c( n.)
`from the loudspeaker is picked up by an array of L
`microphones. Each microphone has its own echo path
`transfer function, and the impulse response of the Zth
`microphone is h,{n). The acoustic echo picked up by
`the ith microphone, d,( n}, is the linear convolution of
`x(n) and h;{n.).
`Suppose an Nth order adaptive filter with coefli—
`cients w,,-( n) and output y,(n) is used to cancel the Eth
`channel echo d,(n); the error at the 3th output is
`given by
`
`erinvl : dri-W} _ yrinl = dill”)
`N—]
`
`‘ Z wrr{”}I(fl—i}.
`[-0
`
`(48)
`
`Dr
`
`loud spcalrcr
`
`receive in
`
`FIG. 4. Block diagram of partial adaptive process.
`
`RTL607_1027-0003
`RTL607_1027—0003
`
`where I is from 1 to L. In order to reduce the complex-
`ity of this echo canceller system, we can break each
`filter into two sections. Therefore Eq. (4a) becomes
`
`Nl—l
`
`e,(n} = d,(n) — Z w,,-{n)x{n -1")
`i=0
`
`‘ E1 we.-ifllxln - 5). Mb)
`i=Nl
`
`Equation (41)) is identical to (tie) except that the
`adaptive filter w:.-( n) now is considered as two filters
`each with order N1 (<N)andN2 { =N—N1),respec-
`tively. The first section is a transversal filter that
`spans the first few hundred taps of the echo impulse
`response, and the second section approximates the
`remainder or tail. Based on Fig. 4, Eq. (4h) can be
`modified as
`
`€:(n)=€i(nl—y}fnl.
`
`(5a)
`
`Nl—1
`
`9201} = dim) - Z wr.-{n)x(n - i},
`[=0
`
`(513)
`
`N—l.
`
`Iii"-l = Z wt.-(nlxln — fl,
`i-N1
`
`where y}(rr} is the output of the tail filter.
`Since the microphone selection unit actuates one
`microphone at a time. and most of the echo energy is
`concentrated in the early portion of the impulse re-
`sponse, much of the computational power is wasted in
`calculating those insignificant coefficients of the tail
`filters. A different approach which uses a single tail
`filter or called the auxiliary filter (A W(z)} with out-
`put y}(n} to concatenate with the first stage filters
`W,(z}, I = 1, 2, .
`.
`.
`, L. In other words, this auxiliary
`adaptive filter is appended to one of the L small filters
`corresponding to the actuated microphone,
`thus
`forming a single large adaptive filter, as shown in Eq.
`I[4b) . This large adaptive filter is fully updatedto per
`form the echo cancellation, while the other L - 1
`small adaptive filters are also updated to keep track of
`the significant changes in the acoustic echo path of
`these L — 1 inactive channels. When channel switch-
`
`ing occurs, the microphone selection unit resets all
`the coeflicients ofA W{ 2) to zero and starts to update
`AW(z) again.
`This technique will have certain advantages over
`the switching method proposed in Ref. [7 ] . Assuming
`eight microphones are used, and the order of each
`
`

`
`W,{z} is 500 and the order of the auxiliary filter,
`A Wlz), is 2500. This technique uses less than 7000
`words of memory compared with 24,000 words re-
`quired in [7]. Furthermore, since the filter coeffi-
`cients for those inactive channels are updated, a dy-
`namic system which has a good performance in real
`environment can be achieved.
`
`Simulation was performed in a four—microphone
`system and the result is shown in Fig. 5. In this figure,
`the symbol ‘"0" indicates the occurrence of channel
`switching. In this simulation. the echo path transfer
`function is assumed to be time-invariant and white
`
`noise is used as the input signal, I( n }, instead of real
`speech. During each receiving period, one channel
`was active, hence. the auxiliary filter AW[z} is com-
`bined with the corresponding w,[ rt) to produce a large
`adaptive FIR filter with order N = 3000. This large
`filter is used for echo cancellation, while the other L —
`
`1 adaptive filters with orders N1 = 500 are updated for
`tracking purposes. Figure 5 shows that there is about
`10 dB of echo return loss enhancement (ERLI-3} at
`
`the incident of channel switching, because the 500
`taps of the L filters were already in optimal condition.
`A much higher ERLE improvement can be achieved if
`the echo paths have faster changes.
`
`4. T||VlE—WElGHTED LMS ALGORITHM
`
`As shown in Section 3, there is at least 10 dB of
`ERLE achievement with the filter order at 500. A
`
`filter order of 1000 is required to achieve 18 dB of
`ERLE. Thus, the extra ERLE will cost more compu-
`tation. Besides this heavy computational burden, the
`slow convergence ofa high order adaptive filter is also
`problematic. Several algorithms were developed to
`improve the convergence speed by using the tap selec-
`tion method [9,10] and by using an exponential step
`
`Echo return loss enhancement for MMAEC.
`
`RTL607_1027-0004
`RTL607_1027—0004
`
`TABLE 1
`
`Comparison of Mathematical Operation
`for Adaptive Algorithms
`
`Cunvn-
`lution
`
`Adapta-
`lion
`
`Standard
`LMS
`Iurder N,f2l
`T“?-LM-"i
`lorder N)
`
`Miiltipliratiun
`Addition
`Multiplication
`Addition
`
`N/2
`IN/2} - 1
`N
`N - 1
`
`{N'/'.!} + 1
`N12
`[Iv/‘ii + I
`NM
`
`[5 Nf4|1 1
`(5 N14! -1
`
`size algorithm [11]. In this paper, based on the expo-
`nential decay characteristics of acoustic echo impulse
`response, an alternative approach called the time-
`weighted LMS algorithm is developed. This algo-
`rithm is effective both in convergence speed and com-
`putational savings.
`Considering an adaptive filter of order 1000 (corre-
`sponding to ERLE of about 18 dB}, we can split these
`1000 filter coefficients into M sections such that each
`
`section has length N1, N2, N3, ..., NM. For each
`sampling period, only one section’s coeflicients are
`updated. The simplest updating strategy is to update
`sections in their sequential order. This sequence will
`be repeated after updating the NMth section and can
`be expressed as
`
`N1,N2,...,NM;N1,N2,...,NM;....(6a)
`
`There are alternative updating strategies. For exam-
`ple, one can update the N1 section more often than
`others by using the following updating sequence, for
`example:
`
`N1, N1, N2, N3, .
`
`.
`
`.
`
`, NM;
`
`N1,N1,N2,N3, ...,NM;
`
`{Sb}
`
`This is a time-weighted sequence and there are vari-
`ety of sequences we can choose depending on applica-
`tions.
`
`To illustrate the advantage of the TW-LMS algo-
`rithm, two simulations are carried out. The first simu-
`lation compares the TW-LMS with the standard
`LMS. A filter of order N = 1000 is used for the TW-
`
`IJMS algorithm. This N is evenly divided into four
`sections and each has 250 coefficients. Considering 10
`consecutive sampling periods as a cycle, the number
`of times used for updating N1, N2, N3, and N4 is in
`the ratio of 5:3:1:1. For the standard LMS algorithm,
`a filter of order N/‘2 : 500 is used and all the filter
`coefficients are updated at a time. The number of
`multiplications and additions in each case is listed in
`Table 1. From this table, it is concluded that the TW-
`
`

`
`LMS algorithm uses almost the same computation as
`the standard LMS algorithm when N is large.
`Figure 6 shows the computer simulation result. In
`this figure, the upper curve is the ERLE obtained by
`the TW-LMS with N = 1000. while the lower curve is
`for the standard LMS with N/2 = 500. From this
`figure and Table 1, we show that by using the TW-
`LMS algorithm, we can implement a filter of twice the
`length to achieve 8 dB of improvement over the stan-
`dard LMS algorithm, but introduces only one quarter
`more computation. This TW-LMS algorithm can be
`used in the first section of PAP filters. W,(z). as
`shown in Fig. 4 to improve the transient performance
`(Fig. 5} from 10 to 18 dB. Also, this algorithm can be
`employed in the tail filter AW-(2) to further reduce
`the computational requirement.
`In the second simulation, the ERLE of the TW-
`LMS algorithm is compared with the traditional
`LMS algorithm where the adaptations of sections N1,
`N2, N3, and N4 have equal weight. Figure 7 shows the
`computer simulation result in both cases. In this simu-
`lation, the TW-LMS again uses the adaptation ratio
`5:3:1:1 for these four sections. and the traditional
`LMS uses the ratio 121:1: 1. From this figure, it is obvi-
`ous that the TW-LMS algorithm has a faster conver-
`gence rate compared with the traditional LMS algo-
`rithm. Actually, the slopes are 12 dB/ 10,000 samples
`and 8 dB/10,000 samples, respectively. In the TW-
`LMS case, 80% of the adaptation time is used on the
`first two sections N1 and N2. These 500 filter coeffi-
`
`cients cover the first 62.5 msecs of the impulse re-
`sponse which is contributed by direct coupling and
`earlier refiections. The faster convergence ofthe TW-
`LMS algorithm is important in real-time acoustic
`echo cancellation applications, since the room envi-
`ronment changes as the result of the movements of
`the people.
`
`sample nu mhcr
`
`4
`
`:10‘
`
`FIG. 6. Comparison ofthe TW —LMS and the standard LMS algo-
`
`RTL607_1027-0005
`RTL607_1027—0005
`
`SEI5E8II
`
`an
`
`ERLE(dB)
`
`I
`
`£135“.
`.:':=.-
`J:-._" Equal we1'gl1|ingl.MS_
`
`L5
`
`2
`
`sample nu.rntx:r
`
`FIG.
`case.
`
`'3". Comparison of the TW—LMS and the traditional LMS
`
`The dynamic {or time-varying} behavior of im-
`pulse response due to the movement of people in the
`room is a complicated problem. In acoustics analysis,
`the impulse response ofacoustic path can be classified
`into three categories as direct sound, earlier reflec-
`tion, and long—term reverberation [12,13]. In princi-
`ple, the earlier reflection involves the first and second
`reflections from the object existing in the room.
`Hence for a conference room of size about 8 m long,
`the earlier echo takes about 47 msec (16/340 secs).
`Since the direct sound and the earlier reflection are
`
`affected more significantly by the environmental
`change in the room than the long-term reverbera-
`tions, it is desirable to weight heavier on the first por-
`tion of the adaptive filter coefficients so that it can
`track the change of the echo path. This is the advan-
`tage of using the TW—LMS algorithm to replace the
`traditional LMS algorithm.
`
`5. AEC USING COMBINATIONS OF ADAPTIVE
`FIR AND IIR FILTERS
`
`In this section, an alternative structure which com-
`bines adaptive FIR and HR filters is proposed. In the
`multiple microphone echo canceller system described
`in Fig. 4, an auxiliary filter, A Wfz) is assigned to one
`of the L first-stage filters according to the micro-
`phone selection unit. This A W(z} is a high order FIR
`filter since it is used to model the tail part ofthe echo.
`Now considering the situation that AW(z) is an [IR
`filter with much lower order to perform the same echo
`cancellation as an FIR filter. The resultant echo can-
`
`celler for each echo path is shown in Fig. 8.
`In Fig. 8, the FIR filter with length N1 is used to
`
`

`
`H(z) =
`
`=1/(1— §ja,.z"'),
`,'..1
`
`14(3)
`
`(9)
`
`where 0, are the coefficients ofthe pth order IIR filter.
`This equation can be expressed as
`
`N1—l
`H(z) A”) = EU w,-z
`
`-
`
`+C'{z)/'(1 —
`
`a,-2"},
`
`(10)
`
`where N1 :- p. This equation states that an all pole
`system can be represented by the combination of FIR
`and HR filters. By comparing Eqs. (8) and [ 10}, it is
`clear that onceA [ 2) reaches optimal solution, its coef-
`ficients Lu:-' will equal to those of h,- for E from Oto N1 —
`1, as expected, and those tail portions ofthe 15,- will be
`expressed by the second term of Eq. ( 10) . Using Eqs.
`{9} and (10), we get [14]
`
`.
`
`(12)
`
`Z-N]
`
`to
`where C(z) covers only the terms from Z" N’
`Z "M 9”. Equations (11) and ( 12) give the transfor-
`mation from the optimal weights to,‘ to (1, and (‘(2 ). It
`is important to have my close to their optimal values,
`so a small step size ,u is preferred. This model has the
`advantage of simple, less computation (total of p2
`multiplications for the application of Eqs. (11) and
`( 12)} and stable statistically [15]. One disadvantage
`of this model is that the oversimplified all-pole model
`can not describe the properties of the zeros of the real
`acoustic echo path.
`
`5.2. ARMA Modeling of Echo Path
`In ARMA modeling, we use an IIR filter with the
`form Biz)/A{z) to model the transfer function of
`echo path, H(z}, i.e.,
`
`FIG. 8. Basic structure of new acoustic echo canceller.
`
`model the first N1 taps of the impulse response of the
`echo path, and the adaptive IIR filter is used to model
`the tail of the impulse response. Since the HR filter
`has a longer impulse response than the FIR filter for
`the same number of coefficients, the total number of
`taps needed for this combined FIR and HR system is
`much less than that using a single large FIR filter.
`Two IIR filter structures are considered. The first
`
`one uses an autoregressive (AR) model and the other
`uses
`a general
`autoregressive moving average
`{ARMA} method. The corresponding mathematical
`derivation in each case is given in subsections 5.1 and
`5.2. In subsection 5.3, simulation results for both im-
`plementations are shown and their performances are
`compared.
`The transfer function of the room acoustic echo
`
`path is
`
`H(2)'— Zh,-2"",
`{=0
`
`[7_l
`
`is the impulse response of the echo path.
`where h,-
`Equation (7) can be partitioned in two parts as
`511-1
`1.
`
`H{z)= Z h,-z“'+ 2 11,2“.
`J=I}
`r'=N1
`
`(3)
`
`The first part of the impulse response can be modeled
`by an N1—tap FIR filter and the long—tail portion can
`be modeled by an HR filter. While the FIR filter coefli-
`cients can be updated iteratively using the LMS algo-
`rithm, the adaptation of the adaptive IIR filter suffers
`from a stability problem.
`The following subsections describe how to obtain
`the [IR filter coefficients from the Nlth order FIR
`
`filter coefficients Without directly implementing the
`adaptive IIR filter.
`
`5.1. Autoregressive Modeling of Echo Path
`
`is assumed
`it
`In autoregressive (AR) modeling,
`that the echo path H(z) is modeled by an all-pole
`adaptive filter 1/44(2) with the form
`
`RTL607_1027-0006
`RTL607_1027—0006
`
`

`
`This is referred as pole—zero system with q zeros andp
`poles. Again we can express B(z)/A{z) in t.wo parts
`85
`
`BL?) L N1—1
`A{z) — 2) LL’|'Z
`
`4
`
`P
`
`.
`
`- Z a,-2")
`j=l
`
`(14)
`
`In the same concept, when these w,- reach their opti~
`mal values, they can describe the first N1 terms of the
`room impulse response. The second term is an HR
`filter used to model the long echo tail. By comparing
`Eqs. (13) and (14), and by lettingp = q, these IIR
`coefficients can be related to the w,- of the FIR filter
`with the following expressions {derived in Appen-
`dix):
`
`u"'p+l
`U-"p+2
`
`wzp
`
`ZNI
`
`In Eq_ { 15 ) . the shifted nature of the columns ofthe
`matrix containing Lu, guarantees the solution of a,- .
`Note that Eqs. { 12) and I 16} have similar expressions
`
`in the sense that all the zeros terms (in C(z) or D(z ))
`are given by w, and a,-. But their values are totally
`different even for the same N1 and p.
`This pole—zero model, in comparison with the all-
`pole model, has the advantage of more closely replicat-
`ing the real system. But, some problems still exist.
`First, the introduction of zeros in the model leads to a
`p by p matrix in Eq. (15), and there will be p3 opera-
`tions needed to solve for a,-, while in Eq. (11) the
`all—pole system only needs pg operations. This could
`be a serious problem when p is large. Second, the per-
`formance of this model is largely dependent on the
`choice ofq, the number of zeros terms in the HR filter,
`which is generally unknown in real applications.
`
`5.3. Simulation Results
`
`To study the behavior of the AR and ARMA mod-
`els, a simple testing transfer function is used. It has
`the form
`
`0.1
`
`H(z)=
`
`‘l — 0.224 — 0.224
`+ 0.353 + 0.52“ —- 0.4'5
`
`Both models are used to cancel the echo produce by
`this transfer function. The learning curve for the
`ARMA model (N1 = 32 andp = 5) is plotted in Fig. 9.
`Note that. there is about 100 dB mean squared error
`reduction as the HR is introduced.
`
`Different combinations of N1 andp are used to test
`the performance of AR and ARMA model, and results
`are summarized in Table 2. The AR model provides
`over 100 dB echo cancellation for p 2- pg, where p,, is
`the number ofpoles in the given system, H{z} . On the
`other hand, the ARMA model cannot perform the
`
`3000
`
`4000
`
`5000
`
`it-brat]. on nurnb-er
`
`FIG. 9.
`
`Learning curve of ARMA model,
`
`RTL607_1027-0007
`RTL607_1027—0007
`
`

`
`TABLE 2
`
`TABLE 3
`
`Performance Comparison of AR and ARMA Models
`
`AR model
`
`ARMA model
`
`Summary of Performance of ARMA Model for Two
`Transfer Functions Given in Eqs. (18) and (19)
`
`'
`
`Diverge
`-100 dB
`-100 dB
`- ms dB
`-100 dB
`-100 dB
`
`Diverge
`— 103 dB
`Diverge
`Diverge
`— 96 dB
`Diverge
`
`p
`
`For H, [2]
`
`For H, [2]
`
`-—
`IIH no effect
`-90 dB
`-80 dB
`Diverge
`—
`
`Diverge
`
`Diverge
`—
`HR no effect
`Diverge
`100 dB
`Diverge
`Diverge
`-110 dB
`
`N1
`
`32
`32
`32
`32
`50
`50
`
`modeling except in cases when N1 = 32, p = 5 and N1
`= 50, p = 6.
`Next, two pole-zero transfer functions are given to
`test the performance of AR and ARMA models. One
`of them has equal number of poles and zeros with the
`form
`
`H¢(z)
`
`__
`
`1 — 0.232" + 0.32" ~ 0.12 '3 -+ 0.12“ + 0.12"“
`1 — 0.022" — 0.022” + 0.32‘-" + 0.52“ — 0.42“ '
`
`(18)
`
`The other transfer function which has unequal num-
`ber of poles and zeros is given by
`
`u 2) —
`
`1 — 0.232” + 0.32‘? — 0.12”
`+ 0.12“ + 0.12 — 0.124‘ + 0.1:"?
`_
`,
`H
`l — 0.022 I — 0.022 ‘I + 0.32 3
`+ 0.52"‘ — O.-42-5
`
`.
`
`(19)
`
`Results show that the ARMA model has good per-
`formance for N1 = 32, p = 5 or 6. similar to the Fig. 9,
`while the AR model diverges all the time. Table 3
`summarizes the performance of ARMA model at dif-
`ferent values of N1 andp.
`This ARMA model was then applied to a real
`acoustic system. The room acoustic transfer function
`was a 25-pole and 25—zero system (modeled by a
`curve-fitting method on the HP3563A control sys-
`tems analyzer). By taking N1 = 128 and q = p = 25,
`the adaptive FIR coefficients were first updated for
`6000 iterates to reach their optimal values, then the
`HR filter was introduced. Results is presented in Fig.
`10. It is shown that there are additional 20 dB of re-
`
`duction is obtained when the IIR portion is intro-
`duced. But when using N1 = 128, q — p = 24 or 26 in
`the ARMA model, the system diverges.
`Simulation results show that neither the AR nor
`
`the ARMA model can provide a satisfactory solution
`
`600
`
`300
`
`1000
`
`1200
`
`Time (msoc)
`
`FIG. 10. Acoustic echo cancellation using ARMA.
`
`W
`
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`

`
`in the complicated real system where the number of
`poles and zeros are unknown in advance. As shown in
`the Appendix, the choice of forward terms q affects
`the set of equations to be used for calculating a,- from
`w,-. This problem was mentioned by several authors
`regarding filter design problem [16—18].
`
`ONCLUSION
`
`This paper presents a partial adaptive process
`which uses two sections of filters to model the echo
`
`path. This technique uses less memory compared with
`the switching method. Furthermore, since the filter
`coetficients for those inactive channels are updated, a
`dynamic system which has at least 10 dB of ERLE
`during the instant of channel switching can be
`achieved.
`
`Based on the exponential decay characteristics of
`the echo path impulse response. a TW—LMS has been
`developed. This method divides the filter coefficients
`into sections, and the adaptation time of these sec-
`tions is weighed. Using TW-IJMS, a higher ERLE im-
`provement is obtained by doubling the filter size, but
`introducing only a small amount of extra computa-
`tion.
`
`The combination ofadaptive FIR and HR filters for
`acoustic echo cancellation is developed. This method
`tends to describe the long-tail feature of the impulse
`response using an all-pole or pole-zero model, thus
`resulting in a smaller order FIR and HR filters. Simu-
`lation results show that this method has the attrac-
`
`tive feature of saving computation, but the stability
`problem requires further research.
`
`APPNDIX: DERWATION OF E08. (15) AND (16)
`
`The transfer function is written in z~transform as
`
`= E 5.-2-‘/(1 -
`
`a,-2").
`
`(A1)
`
`Assume we can write it in two parts, an FIR and an
`[IR filter:
`
`N—l
`8(2) = Z w,-z"'+D{z),’(1 — E oi-2").
`A(z)
`I"-=0
`,:'-—I
`
`{A2}
`
`These two equations lead to a set of equations for
`equal powers of 2 as
`
`tun
`
`—a,w,, + w,
`
`—[I2LU0 "‘ HILL‘, + [132
`
`‘ --a1wq + w_.',+,
`
`' “a1wq+1 ‘I’ wq+2
`
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`

`
`. Widrow, B., and Stearns, S. D. Adaptive Signal Processing.
`Prentice—Hall, Englewood Cliffs, New Jersey, 1985.
`. Caraiscos, C., and Lin, B. A roundoff error analysis of the LMS
`adaptive algorithm. IEEE '1":-ans. Acoust. Speech Signal Pro-
`cess. ASSP-32, 1 {Feb. 1934]. 34-41.
`. Gitlin, R., et ol.. On the design of gradient algorithms for digi-
`tal implemented adaptive filters. JEEE Tran.-;. Circuit Theory
`CT-20. 2 (Mar. 1973], 125-136.
`_ Oikawa, I-1., et al., A new echo canceller realized by high perfor-
`mance digital signal processor. In IEEE International Sympo-
`sium on C'ircm‘t.-3 and Systems, 1988. pp. 1329-1332.
`. Mitchrll, D., et al., General transmission considerations in tele-
`phone conference systems. IEEE Trans. Comm. Tech. 16, 1
`{I968}, 163.
`. Koizumi, N., Makino, S., and Oikawa. H. Acoustic echo can-
`celler with multiple echo paths. J. Aconst. Soc. Jpn. {E} 10, 1
`{I989}. 39-45.
`. Oikawa, H.. Koizumi, N., and Mal-Lino, S. Audio teleconferenc-
`ing set with multipath echo canceller. Rev. Elect. Comm. Lab.
`36. 2 (1983). 217-223.
`. Oikawa, H.. Minami, S., and Saeki, '1‘. A new echo canceller
`realized by high performance digital signal processor. In Proc.
`t(‘A.‘3SP 88, 1988. pp. 1329-1332.
`. Kawamura, S., and I-Iatori, M. A tap selection algorithm for
`adaptive filters. In Proc. ICASSP 86, 1988, pp. 2979 -2981.
`. Madisetti, V. K.. Messerschmitt. D. G., and Nordstrom. 1\'.
`I)ynamicalIy—reduced complexity implementation ofecho can-
`celers. In Prt.-L‘. ICASSI’ 86, 1986. pp. 1313-1316.
`. Malcino, S., and Kaneda, Y. Acoustic echo canceler algorithm
`based on the variation characteristics of a room impulse re-
`sponse. In Proc. IEEE, 1990, pp. 1133-1136.
`. Kuttrulf, H. Room Acriustics. Applied Science, London, 1979.
`. Rossing, T. D. The Science of Sound. Addison—Wesley, Read-
`ing, MA, 1932.
`
`'
`
`'
`
`. Downing, C. P., Boland, F. M., and F'oIey,J. B. Improved noise
`canceller performance by means of an adaptive arrangement of
`HR and FIR filters. In IEEE Internationai Conference on
`Acoustics, Speech, and Signal Processing. 1989, Vol. 3, pp.
`2005-2008.
`
`. Burrus, C. S., and Parks, T. W. Time domain design of recur-
`sive digital filters. IEEE Trans. Audio Elect. AU-18 (June
`1970l. 134-141.
`. Jackson, L. B. Digital Filters and Signal Pwcrrssing, 2nd ed.
`Kluwer, Dordrecht, I989.
`. Evans, A. G., and Fish], R. Optimal least square time—domain
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`AU-21 (Feb. 19T3), 61-65.
`
`. Jackson, L. B. Simple, effective MA and ARMA techniques. In
`Proceedings,
`IEEE International Conference on Acoustics.
`Speech. and Signal Processing, April 1983, pp. 14264429.
`
`SEN M. KUO received his 311.8. and Ph.D. degrees from the
`Dept. of Electrical Engineering, University of New Mexico. in 1983
`and 1985. respectively. He joined the Department of Electrical En-
`gineering, Northern lllinois University, as an assistant professor.
`He is engaged in research on adaptive filtering applications and
`implementations. His research interests are in the areas of active
`noise and vibration control, acoustic echo cancellation, digital
`hearing aid, adaptive noise cancellet ion, and audio signal process-
`ing. He serves as a consultant to Texas Instruments, Motorola,
`General Motors, DuKane, and Teleconferencing Technology.
`
`JIER CHEN received the B.S. degree in physics from the Univer-
`sity of Birmingham, England, in 1983, and the M.S. degrees in
`physics and electrical engineering from the Northern Illinois Uni-
`versity in 199] and 1992, respectively, Currently, he is a research
`and development engineer at Shore Brothers Inc., Evanston,
`Illinois.
`
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