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

Single-channel hands-free teleconferencing platforms have gotten well known. which will improve the conversation caliber of those structures, increasingly more stereophonic sound units with loudspeakers and microphones are deployed. a result of coupling among loudspeakers and microphones, there is robust echoes, which make real-time conversation very tough. the way in which we all know to cancel those echoes is through a stereo acoustic echo canceller (SAEC), which 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 procedure with advanced random variables due to the commonly linear version. From this new handy formula, they re-derive crucial facets of a SAEC, together with id of the echo paths with adaptive filters, double-talk detection, and suppression.

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1 Affine Projection Algorithm (APA) In this section, we briefly derive the affine projection algorithm (APA) that was originally proposed in [1]. We develop it in the WL context. As a consequence, the resulting algorithm is equivalent to the one proposed in [2]. The APA can be seen as a generalization of the NLMS, where the projection order is increased from 1 to P . The clear advantage of the APA over the NLMS is that it may converge must faster thanks to the fact it considers in its update equation both past and current input vectors.

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95) κ (−1 ≤ κ < 1) is a parameter that controls the amount of proportionality in the IPNLMS, and δ is the regularization constant. 98) xH (n)G(n which depends on the new observation d(n). Note that P (n) does not depend on the noise signal. ← − It can be shown that h (n) is a good approximation of the optimization problem: min ← − h (n) 2 ← − ← −H d(n) − h (n)x(n) + δ h (n) . 99) 1 The previous optimization is the regularized version of the minimum 1 -norm ← −H solution of the linear system of one equation d(n) = h (n)x(n).

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