A Perspective on Stereophonic Acoustic Echo Cancellation by Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu

By Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină

Single-channel hands-free teleconferencing platforms have gotten renowned. so that it will increase the conversation caliber of those structures, a growing number of stereophonic sound units with loudspeakers and microphones are deployed. as a result of the coupling among loudspeakers and microphones, there's robust echoes, which make real-time conversation very tricky. the way we all know to cancel those echoes is through a stereo acoustic echo canceller (SAEC), that are modelled as a two-input/two-output method with actual random variables. during this paintings, the authors recast this challenge right into a single-input/single-output approach with complicated random variables due to the generally linear version. From this new handy formula, they re-derive an important features of a SAEC, together with id of the echo paths with adaptive filters, double-talk detection, and suppression.

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2 The misadjustment is defined as [3] M= Jex (∞) . 30) μ tr Rx , μ small. 2 The misadjustment measures how well μE [x(n)e∗ (n)] is approximated by μx(n)e∗ (n) at the steady state. 32) where is the a posteriori error signal, computed after the filter is updated. This intuitively makes sense since (n) contains more meaningful information than e(n). This condition is necessary for the LMS to converge to the impulse response of the system but not sufficient. However, it is very useful for finding the bounds for the step size μ.

With a judicious choice of the elements of G and making them dependent on the coefficients of the acoustic impulse response, we can promote sparsity. 80) is convenient to use in adaptive filters. References 1. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series. New York: John Wiley & Sons, 1949. 2. S. Haykin, Adaptive Filter Theory. Fourth Edition, Upper Saddle River, NJ: PrenticeHall, 2002. 3. M. M. Sondhi, D. R. Morgan, and J. L. Hall, “Stereophonic acoustic echo cancellation– An overview of the fundamental problem,” IEEE Signal Process.

Fourth Edition, Upper Saddle River, NJ: PrenticeHall, 2002. 3. B. Widrow, J. M. McCool, M. G. Larimore, and C. R. , “Stationary and nonstationary learning characteristics of the LMS adaptive filter,” Proc. of the IEEE, vol. 64, pp. 1151–1162, Aug. 1976. 4. -I. Nagumo and A. Noda, “A learning method for system identification,” IEEE Trans. Autom. Control, vol. AC-12, pp. 282–287, June 1967. 5. J. Benesty, C. Paleologu, and S. Ciochin˘ a, “Proportionate adaptive filters from a basis pursuit perspective,” IEEE Signal Process.

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