ADAPTIVE DIGITAL FILTERS AND ECHO CANCELERS

Abstract: An adaptive digital filter capable of generating an arbitary transfer function and suitable for use in an echo canceler, has its scaler coefficients (a m , b m , R m ) and variable scaler coefficients (C m , D m ) selected such that the convergence characteristics of the filter are maintained irrespective of whether the input signal to the filter is a white signal or a non-white signal.

Description: Technical Field This invention relates to adaptive digital filters capable of generating an arbitrary transfer function having a fast rate of convergence, suitable for use in an echo canceler. Background Art Recent rapid progress in digital signal-processing technology has created great interest in adaptive digital filters due to their wide range of applications. Typical of these applications in system identification, which is a process of estimating an unknown system characteristic from input and output data. Such a system is described in the Applicants EP-A-87306101.4. The adaptive digital filter disclosed therein displays excellent convergence characteristics when the input signal is a white-noise signal. When the input signal has a non-white characteristic, as in a voice signal, the outputs from each section of the filter are not orthogonal, and their mean square values are unequal, so the convergence characteristics of the variable coefficients are degraded. The Invention The invention provides an adaptive digital filter comprising M basic sections (wherein M is a positive integer) each having a second-order recursive filter with scaler coefficients a m and b m , a first coefficient scaler for multiplying a first one of a zeroth-order delayed output and a first-order delayed output from the second-order recursive filter by a first coefficient, a first variable-coefficient scaler for multiplying the first one of the zeroth-order delayed output and the first-order delayed output from the second-order recursive filter by a first variable-coefficient, a first adder for adding the output from the first scaler and a second one of the zeroth-order delayed output and the first-order delayed output from the second-order recursive filter, a second variable-co-efficient scaler for multiplying the output from the first adder by a second variable-coefficient, and a second adder for adding the outputs from each of the variable-coefficient scalers, characterised in that the scaler coefficients a m and b m are selected such that the poles of the second order recursive filter are located near the unit circle in the Z plane, and the first variable coefficient and the second variable coefficient are selected such that the mean square values of the first one of the zeroth-order delayed output and the first-order delayed output from the second-order recursive filter and the output from the first adder are equal. In a preferred arrangement the first one of the outputs from the second-order recursive filter is a first-order delayed output and the second one of the outputs from the second-order recursive filter is a zeroth-order delayed output. In another the first one of the outputs from the second-order recursive filter is a zeroth-order delayed output and the second one of the outputs from the second-order recursive filter is a first-order delayed output. The M basic sections are preferably connected in series. M-1 of the M basic sections may have a second-order non-recursive filter, the output of which is conencted to the second-order recursive filter of the next section. Alternatively the M basic sections may be connected in parallel. The outputs from the second adder of each section may be added to produce the final output from the filter. Drawings: Figure 1 is a schematic diagram showing in principle the identification of an unknown system by use of an adaptive digital filter; Figure 2 is a schematic diagram showing a teleconferencing system employing an echo canceler comprising an adaptive digital filter as in Figure 1; Figure 3 shows a configuration of an adaptive digital filter as in our EP Application mentioned above; Figure 4 shows the adaptive digital filter of Figure 3 without scalers to explain the selection of coefficients a m and b m ; Figure 5 shows the m-th basic section in Figure 3 to explain equalization of mean square values of g m (k) and V m (k); Figure 6 shows in combination the configuration of Figures 4 and 5; Figures 7 to 10 show adaptive digital filters of different embodiments of the invention; and Figures 11 and 12 show echo cancelers of further embodiments of the invention. Best Mode With particular reference to Figure 1, identification means comprise a signal input terminal 11, an error output terminal 12, an unknown system 13, and adaptive digital filter (ADF) 14, and an adder 15. In the figure x(k) is the input to the unknown system 13 and the adaptive digital filter 14 at time k, y(k) is the output from the unknown system 13 at time k, y and(k) is the output from the adaptive digital filter 14 at time k, e(k) is the estimation error at time k, H(z) is the transfer function of the unknown system, and H and(Z) is the transfer function of the adaptive digital filter 14. In the configuration shown, if the evaluation function is J = e(k)², then when J = O the adaptive digital filter 14 is regarded as correctly estimating the characteristic of the unknown system 13. Figure 2 is a schematic diagram of a teleconferencing system employing an echo canceler. This system comprises a pair of microphones 21-1 and 21-2, a pair of loudspeakers 22-1 and 22-2, a pair of echo cancelers 23-1 and 23-2, a pair of transmission lines 24-1 and 24-2, and a pair of adaptive digital filters 25-1 and 25-2, and includes a pair of acoustically coupled paths 26-1 and 26-2. In most teleconferencing systems the loudspeaker and microphone shown in Figure 2 are integrated into a single unit called a voice terminal. This gives rise to an acoustic coupling between the loudspeaker and the microphone: the signal output from the loudspeaker is coupled into the microphone and greatly degrades the quality of the voice transmission. In Figure 2 there are acoustic coupling paths, labelled 26-1 and 26-2, between the loudspeaker 22-1 and the microphone 21-1, and between the loudspeaker 22-2 and the microphone 21-2, but the echo cancelers 23-1 and 23-2 act to eliminate the signal coupled from the loudspeaker into the microphone. Our EP Application EP-A-87306101.4 mentioned above shows in Figure 3 hereto the first of these adaptive digital filters. This adaptive digital filter comprises M basic sections connected in series (where M is a positive integer). Basic sections 1 through M-1 each comprise a second-order recursive digital filter and a second-order non-recursive digital filter. Basic section M, the final section, comprises a second-order recursive digital filter. Adjacent basic sections are connected by scalers that multiply by Q m and by 1/Q m (m = 1 to M). Each basic section also has a first-order non-recursive digital filter comprising a scaler R m for multiplying the first-order delayed output u m (k-1) by the coefficient R m , an adder 31 for adding the result to the Oth-order delayed output u m (k), a scaler S m for multiplying the output of the adder 31 m by the coefficient S m , a variable-coefficient scaler C m (k) for multiplying the result u m (k) by a variable coefficent c m (k), a variable-coefficient scaler d m (k) for multiplying the first-order delayed output u m (k-1) by a variable coefficient d m (k), and an adder 32 m for adding the outputs of the two variable-coefficient scalers c m (k) and d m (k). The outputs from the adders 32 m are added one after the other and the output from the adder 33 M is the output y(k) of the filter with respect to the input x(k). The coefficients Q m of the scalers Q m (m = 1 to M) are chosen so that the mean square values of the first order delayed outputs u m (k-1) (m = 1 to M) are equal to the mean square value of the input signal x(k) (a white-noise signal). The coefficients S m of the scalers S m (m = 1 to M) are chosen so that the mean square values of their outputs u and m (k) (m = 1 to M) are equal to the mean square value of the input signal x(k). The coefficients R m of the scalers R m (m = 1 to M) are chosen so that when x(k) is a white-noise signal, the signals u and m (k-1) and u and m (k) (m = 1 to M) are orthogonal. These selections increase the rate of convergence of the variable coefficients c m (k) and d m (k) (also called the adaptive parameters) of the variable-coefficient scalers. Figure 4 shows the adaptive digital filter of Figure 3 the scaler Q m having the coefficent Q m (m = 1 to M), the scaler 1/Q m having the coefficient 1/Q m (m = 1 to M), and the scaler S m having the coefficient S m . Assume that the input signal x(k) has a white characteristic, and that a circuit with a transfer function F(z) converts this to a signal with a non-white characteristic, which is input to the adaptive digital filter. Let g m (k) be the output of the first-order delay element in the m-th basic section (m = 1 to M), let v m (k) be the sum of g m (k) multiplied by the coefficient R m (m = 1 to M) and the 0th-order delayed output, and let g m (z) and v m (z) be the z-transforms of g m (k) and v m (k). Then: The time average of g m (k) and v m (k) is calculated as follows, where E[.] is the time-averaging operator: The term in Equ. (2) describes an all-pass filter circuit. If f n (z) = z² -a n z + b n and f m (z) = z² - a m z + b m , and a n , a m , b n , and b m are selected so that the roots of f n (z) and f m (z) are located near the unit circle, then: and similarly: where an overbar indicates the complex conjugate. From equations (2) to (4) it follows that: Since the integrand in Eq. (5) matches the case of |F(z)| = 1. which is the case of white noise input to the adaptive digital filter, the contour integral is zero. Therefore: E[g m (k). v n (k)] ≈ 0 (6) The other orthogonality conditions are also approximately satisfied; that is, E[g m (k). v m (k)], E[g m (k).g n (k)] and E[v m (k).v n (k)] can be shown to be approximately zero. Thus if the poles of the second-order recursive digital filter are near the unit circle in the z-plane, u m (k) and u m (k-1) are approximately orthogonal even when the input signal is non-white. Figure 5 shows the m-th basic section (m=1 to M-1) in Figure 3 modified by the addition of a variable-coefficient scaler A m (k) with variable coefficeint A m (k) and a variable-coefficient scaler B m (k) with variable coefficient B m (k). (Similar modifications are also made to the M-th basic section). The purpose of the variable scaler coefficients A m (k) and B m (k) is to equalize the mean square values of the input signals to the scaler c m (k) with variable scaler coefficient c m (k) and the scaler d m (k) with variable scaler coefficient d m (k). A m (k) and B m (k) are accordingly selected as follows: If the well-known learning identification algorithm is used for updating the values of c m (k) and d m (k), then: Combining the scalers A m (k) and C m (k) so that C m (k) = A m (k) c m (k), Eq. (8) becomes: Let: Then from Eqs. (7) and (9): Similarly: If we set D m (k) = B m (k), then from Eqs. (10) and (12): If f m (z) = z² - a m z + b m and a m and b m are selected so that the roots (poles) of f m (z) are located near the unit circle, and the variable scaler coefficients C m and D m are updated by Eqs. (11) and (13), the signals g m (k) and v m (k) will be nearly orthogonal and their mean square values will all be equal; therefore the rate of convergence of the adaptive parameters will be extremely fast. Figure 7 shows a first embodiment based on the principles above. The adaptive digital filter used in this embodiment comprises M basic sections connected in series (where M is a positive integer). The first M-1 basic sections (from 1 to M - 1) each comprise a second-order recursive digital filter and a second-order non-recursive digital filter. The final basic section (M) comprises a second-order recursive digital filter. The output of the second-order non-recursive digital filter is connected to the input of the second-order recursive digital filter in the next section. In addition, the m-th basic section (m = 1 to M) comprises a scaler R m for multiplying the first-order delayed output g m (k) by a scaler coefficient R m , a first adder 1 m for adding the output of the scaler R m to the Oth-order delayed output signal, a first variable-coefficient scaler C m (k) for multiplying the output v m (k) of the first adder 1 m by a variable scaler coefficient C m (k), second variable-coefficient scaler D m (k) for multiplying the first-order delayed output g m (k) by a variable coefficient D m (k), and a second adder 2 m for adding the output of the first variable-coefficient scaler to the output of the second variable-coefficient scaler. An adder 3 m adds the output of the second adder 2 m to the output of the second adder 2 m+1 in the next section, and this process continues through the adder 3 M , from which is obtained the final output y(k) of the filter. The scaler coefficents a m and b m are selected as described above. Specifically, they are determined as follows. If a m and b m are selected so that: then the transfer function H(z) of the adaptive digital filter in Figure 6 will be: where N(z) is a function of C m and D m . If R « 1, then H(Z) ≈ N(z), so that the unknown system can be estimated to be N(z). Let re jϑk be a root of (z 2M ± R). Since r 2M e j2Mϑk + R = 0: r 2M e j2Mϑk = -R=Re jπ. e j2πk (K=0,1,2 ..., 2M-1) hence Similarly, since r 2M e j2Mϑk -R = 0: r 2M e j2Mϑk =R=Re j2πk (k=0,1,2...,2M-1) hence From Eq. (14), hence with the condition that when ϑ ₀ = 0, a m = 0 and b m = -R 1/M (the real root). For example, suppose R = 0.1 and 2M = 100. (Values of this order are required in applications such as echo cancelers). From Eqs. (16) and (17) the pole radius is r = R 1/2M = 0.1 1/100 = 0.9772, which is close to the unit circle. Eqs. (16) and (17) also indicate that the poles are located at equally-spaced angles at the radius r = R 1/2M centered around the origin of the z-plane. The variable-coefficient scaler scalers C m (k) and D m (k) (m = 1 to M) are updated according to Eqs (11) and (13) and a m and b m are selected according to Eq.(19). The output signal from F(z), which becomes the input to the first basic section, is added to the output of the second-order recursive digital filter in that section. The sum, which is the 0th-order delayed output, is multiplied by the coefficient b₁. The result is added to the output of the second-order non-recursive digital filter and sent to the next section. The first-order delayed output g₁(k) is multiplied by the coefficient R₁ and the result is added to the Oth-order delayed signal. The resulting sum V₁(k) is multiplied by the variable C₁(k), the first-order delayed output g₁(k) is multiplied by the variable coefficient D₁(k), and the two products are added. The sum is added to the corresponding sum in the next section. This same process is repeated until the filter ouput y(k) is obtained from the final section M. The output from the unknown system is subtracted from the filter output y(k) in the adder 4 to obtain the residual difference signal (error signal) e k . Figure 8, shows the second embodiment. The scalers R m (m = 1 to M) are inserted in a position reverse to that in the embodiment shown in Figure 7. That is, the 0th-order delayed output v m (k) is multiplied by the coefficient R m , and added to the first-order delayed output in the adder 1 m . The result g m (k) is multiplied by the variable coefficient D m (k). The 0th-order delayed output v m (k) is also multiplied by the variable coefficient C m (k). The two product signals are added in the adder 2 m . Despite this difference in configuration, the adaptive digital filter of the second embodiment functions in the same way as in the first embodiment. Further explanation is therefore omitted here. Figure 9 shows a third embodiment comprising M second-order recursive digital filters connected in parallel. Each second-order recursive digital filter comprises a scaler R m for multiplying the first-order delayed output g m (k) by a coefficient R m , a first adder 1 m for adding the output of the scaler R m to the 0th-order delayed output signal, a first variable-coefficient scaler C m (k) for multiplying the output v m (k) of the first adder 1 m by a variable coefficient C m (k), a second variable-coefficient scaler D for multiplying the first-order delayed output g m (k) by a variable coefficient D m (k), and a second adder 2 m for adding the output of the first variable-coefficient scaler to the output of the second variable-coefficient scaler. An adder 2 m adds the output of the second adder 2 m to the output of the second adder in the previous section 2 m -1 (not shown in the figure). The final output of the filter is obtained from the adder 3 M . The input signal applied to the input terminal is fed to all of the second-order recursive digital filters. This input is added to the value of the first-order delayed output g m (k) multiplied by the coefficient a m minus the value of the second-order delayed output multiplied by the coefficient b m . The first-order delayed output g m (k) is also multiplied by the coefficient R m and added to the 0th-order delayed output in the adder 1 m . The output v m (k) of this adder 1 m is multiplied by the variable coefficient C m . The first-order delayed output g m (k) is also multiplied by the variable coefficient D m . The two product signals are added in the adder 2 m , and the sum is output to the adder 3 m . The adder 3 m adds the output of the adder 2 m to the corresponding output in the preceding section and feeds the result to the corresponding adder 3 m+1 ) in the next section. The final output of the filter is obtained from the adder 3 M . a m and b m (m = 1 to M) are selected so that the input signals to the variable-coefficient scaler C m (k) and D m (k) are approximately orthogonal, and their mean square values are all equalized by the variable-coefficient scaler C m (k) and D m (k). Figure 10 shows one basic section of the fourth embodiment of the invention. In this embodiment, the scalers R m (m = 1 to M) are inserted in positions reverse to those in the embodiment shown in Figure 9. That is, the 0th-order delayed output v m (k) is multiplied by the coefficient R m , then added to the first-order delayed output in the adder 1 m . The result g m (k) is multiplied by the variable coefficient D m . The 0th-order delayed output v m (k) is also multiplied by the variable coefficient C m (k). The two product signals are added in the adder 2 m , and the result is added to the corresponding output from the preceding section. The other parts of the embodiment in Figure 10 function in the same way as in the embodiment of Figure 9 and produce the same result. Further explanation is therefore omitted here. A fifth embodiment of the invention is shown in Figure 11. This embodiment is an echo canceler having an adaptive digital filter similar to the embodiment of Figure 9 but also includes a measure providing for the case in which the R in the denominator polynomial 1 ± Rz -2M in Eq. (15) cannot be ignored. The adaptive digital filter with the transfer function H(z) in this figure is identical to the adaptive digital filter in Figure 6. From Eq. (15) the transfer function H(z) of this adaptive digital filter is: A recursive digital filter having a transfer function of 1/(1 ± Rz -2M ) is inserted in series with the unknown system H(z), so: from which it follows that N(z) = H and(z), indicating that N(z) is capable of accurately estimating H and(z). When the adaptive digital filter in this drawing is used in a bidirectional communiction system as shown in Figure 2, since a non-recursive digital filter with the inverse transfer function of 1/(1 ± Rz -2M ) is connected to the output of the adder 4, the transfer function from the signal input point at the microphone to the output terminal (leading to the communication line) is: Hence the signal input at the microphone is reproduced at the output terminal. Let E(z) be the z-transform of e(k) in the drawing and let E and(z) be the z-transform of e and(k). Then: The error signal H and(z) - N(z) is produced at the output terminal, but this quantity is not in question because it is the estimation error. The measure providing for the case in which the R in the denominator polynominal 1 ± Rz -2M in Eq. (15) cannot be ignored, as described in connection with the embodiment of Fig. 11 can be adopted to any of the embodiments of Figs. 8 to 10 as well. Figure 12 shows the configuration where such measure is adopted to the embodiment of Figure 9. The functions are similar to those described in connection with the embodiment of Figure 11.

Claims: An adaptive digital filter (ADF) comprising M basic sections (where M is a positive integer) each having a second-order recursive filter with scaler coefficients a m and b m , a first coefficient scaler for multiplying a first one of a zeroth-order delayed output (v m (k)) and a first-order delayed output (g m (k)) from the second-order recursive filter by a first coefficient (R m ), a first variable-coefficient scaler for multiplying the first one of the zeroth-order delayed output (v m (k)) and the first-order delayed output (g m (k)) from the second-order filter by a first variable coefficient (D m (k),C m (k)), a first adder (1 m ) for adding the output from the first scaler and a second one of the zeroth-order delayed output (v m (k)) and the first-order delayed output (g m (k)) from the second-order recursive filter, a second variable-coefficient scaler for multiplying the output from the first adder by a second variable coefficient (C m (k), D m (k)) and a second adder (2 m ) for adding the outputs from each of the variable coefficient scalers, characterised in that the scaler coefficients a m and b m are selected such that the poles of the second order recursive filter are located near the unit circle in the Z plane, and the first variable-coefficient (D m (k),C m (k)) and the second variable-coefficient (C m (k),D m (k)) are selected such that the mean square values of the first one of the zeroth-order delayed output (v m (k)) and the first-order delayed output (g m (k)) from the second-order recursive filter and the output from the first adder (1 m ) are equal. An adaptive digital filter (ADF) according to claim 1 wherein the first one of the outputs from the second-order recursive filter is a first-order delayed output (g m (k)) and the second one of the outputs from the second-order recursive filter is a zeroth-order delayed output (v m (k)). An adaptive digital filter according to claim 1 wherein the first one of the outputs from the second-order recursive filter is a zeroth-order delayed output (v m (k)) and the second one of the outputs from the second-order recursive filter is a first-order delayed output (g m (k)). An adaptive digital filter of claim 2 or claim 3 wherein the M basic sections are connected in series. An adaptive digital filter according to claim 4 wherein M-1 of the M basic sections has a second-order non-recursive filter, the output of which is connected to the second-order recursive filter of the next section. An adaptive digital filter according to claim 2 or claim 3 wherein the M basic sections are connected in parallel. An adaptive digital filter according to claim 5 or claim 6 wherein the outputs from the second adder (2 m ) of each section are added to produce the final output from the filter. An echo canceler incorporating the adapative digital filter according to any of claims 1 to 7.

Inventors: KOBAYASHI, MASAKI
Applicants: OKI ELECTRIC INDUSTRY COMPANY, LIMITED
Application year: 1987
Main classification: H03H21
IPC codes: H03H21, H04B3