By Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină
Single-channel hands-free teleconferencing structures have gotten renowned. with a view to increase the communique caliber of those structures, progressively more stereophonic sound units with loudspeakers and microphones are deployed. as a result of coupling among loudspeakers and microphones, there is robust echoes, which make real-time verbal exchange very tricky. the way we all know to cancel those echoes is through a stereo acoustic echo canceller (SAEC), which are modelled as a two-input/two-output approach 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 identity of the echo paths with adaptive filters, double-talk detection, and suppression.
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Extra resources for A Perspective on Stereophonic Acoustic Echo Cancellation
L. Gay, “An improved PNLMS algorithm,” in Proc. IEEE ICASSP, 2002, pp. 1881–1884. 23. C. Paleologu, J. Benesty, and S. Ciochin˘ a, “A variable step-size proportionate NLMS algorithm for echo cancellation,” Revue Roumaine des Sciences Techniques – Serie Electrotechnique et Energetique, vol. 53, no. 3, pp. 309–317, 2008. 24. J. Benesty, F. Amand, A. Gilloire, and Y. Grenier, “Adaptive ﬁltering algorithms for stereophonic acoustic echo cancellation,” in Proc. IEEE ICASSP, 1995, pp. 3099–3102. Chapter 5 A Class of Aﬃne Projection Algorithms Aﬃne projection algorithms (APAs) are very good candidates for echo cancellation.
41) is obtained when α0 (n) = α1 (n) = · · · = αP −1 (n) = α. 2), the posteriori error vector becomes (n) = [IP − Dα (n)] e(n). , (n) = 0. 44) that Dα (n) = IP . 41), with the step size α = 1. , v(n) = 0, we deal with an ideal “system identiﬁcation” conﬁguration. In this case, the value of the step size α = 1 makes sense, because it leads to the best performance . , to recover the system noise from the error of the adaptive ﬁlter. 45) where p (n) and ep (n) denote the (p + 1)th elements of the vectors (n) and e(n), with p = 0, 1, .
Both vectors are obviously in the nullspace of P(n). 54) which is not aﬀected by h (n − 1). 51) is that ← − h (n) is, in fact, the minimum 2 -norm solution of the linear system of one ← −H equation d(n) = h (n)x(n). 45). And, of course, h(n) is also a solution of d(n) = h (n)x(n). Therefore, h (n − 1) can be seen as a good initialization of the adaptive ﬁlter since the minimum 2 -norm solution is not the optimal solution. The interpretation  of the NLMS algorithm is the following. First, we ← −H ﬁnd the minimum 2 -norm solution of d(n) = h (n)x(n), which is denoted ← − by h (n).
A Perspective on Stereophonic Acoustic Echo Cancellation by Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină