By Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină
Single-channel hands-free teleconferencing structures have gotten renowned. so that it will increase the verbal exchange caliber of those platforms, an increasing number of stereophonic sound units with loudspeakers and microphones are deployed. due to the coupling among loudspeakers and microphones, there's robust echoes, which make real-time communique very tricky. the way we all know to cancel those echoes is through a stereo acoustic echo canceller (SAEC), which might be modelled as a two-input/two-output procedure with genuine random variables. during this paintings, the authors recast this challenge right into a single-input/single-output approach with advanced random variables because of the generally linear version. From this new handy formula, they re-derive an important points of a SAEC, together with id 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
P − 1. Consequently, XT (n)X∗ (n) + δIP −1 = QP (n) [δIP + ΛP (n)] −1 QH P (n). 31), we get ← − e (n) 2 2 = dH (n)QP (n) IP − ΛP (n) [δIP + ΛP (n)] 2 −1 QH P (n)d(n). 32) without any supporting assumptions on the character of the input signal. 30)] are λP,p (n) ≈ 2Lσx2 , for p = 0, 1, . . , P − 1. 32) can be expressed as ← − e (n) 2 2 = dH (n)QP (n)QH P (n)d(n) δ δ + 2Lσx2 2 . 28) becomes E d(n) 2 2 δ δ + 2Lσx2 2 =E v(n) 2 2 . 36) where y(n) = y(n) y(n − 1) · · · y(n − P + 1) T contains the most recent P samples of the echo signal.
Vol. 47, pp. 864–872, Mar. 1999. 13. A. Mader, H. Puder, and G. U. , vol. 80, pp. 1697–1719, Sept. 2000. 14. -C. Shin, A. H. -J. Song, “Variable step-size NLMS and aﬃne projection algorithms,” IEEE Signal Process. , vol. 11, pp. 132–135, Feb. 2004. 15. J. Benesty, H. Rey, L. Rey Vega, and S. Tressens, “A non-parametric VSS-NLMS algorithm,” IEEE Signal Process. , vol. 13, pp. 581–584, Oct. 2006. 16. D. R. Morgan and S. G. Kratzer, “On a class of computationally eﬃcient, rapidly converging, generalized NLMS algorithms,” IEEE Signal Process.
In the same way, J. : A Perspective on Stereophonic Acoustic Echo Cancellation, STSP 4, pp. 49–62. com 50 5 A Class of Aﬃne Projection Algorithms we deﬁne the P × 1 a posteriori error vector as (n) = d(n) − XT (n)h∗ (n). 2) The APA is obtained as follows: min h(n) − h(n − 1) h(n) 2 subject to (n) = 0. 3) 2 Using Lagrange multipliers, we easily ﬁnd the update equation of the algorithm, which is h(n) = h(n − 1) + X(n) XH (n)X(n) −1 e∗ (n). 4) cancels the a posteriori error vector. Also, by taking P = 1, we ﬁnd the NLMS algorithm derived in the previous chapter.
A Perspective on Stereophonic Acoustic Echo Cancellation by Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină