By Yiteng Huang

Telecommunication platforms and human-machine interfaces have started utilizing a number of microphones and loudspeakers to render interplay extra practical, and extra effective. This increases acoustic sign processing difficulties less than multiple-input multiple-output (MIMO) eventualities, encompassing far-off speech acquisition, sound resource localization and monitoring, echo and noise keep watch over, resource separation and speech dereverberation, etc. The ebook opens with an acoustic MIMO paradigm, constructing basics, and linking acoustic MIMO sign processing with classical sign processing and verbal exchange theories. the second one a part of the e-book provides a unique research of acoustic purposes performed within the paradigm to enhance the basics of acoustic MIMO sign processing.

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In the next subsection, we will show how to compute XF by using the Levinson-Durbin algorithm. 3 Fast Computation of the Condition Number In this subsection, we need to efficiently compute the two norms R / ^ J and R/^^.! • The calculation of the first one is straightforward. Indeed: 40 3 Wiener Filter and Basic Adaptive Algorithms = tr[Ri+i] F = (L-f l)r(O). 45) requires one multiplication only. Consider the matrix G L + 1 = R-L+i where its diagonal elements are PL+I,U, i = 1,2, •••,L-f 1. +i)(L+i) = QL^' The Lth diagonal element of G L + I is ^L+I,LL = ^Z-i + Q1}^\,L' Continuing the same process, we easily find: L with ^0 = r(0).

A diverse multichannel system is irreducible. Otherwise, a multichannel system whose impulse responses share common zeros can be decomposed into two or more sequential subsystems, which have either single or multiple channels. 11) HM{Z)}^0, where gcd{} denotes the greatest common divisor of the polynomials involved. Then we have Hn(z) = C{z)H'^(z), n = l , 2 , . - . 12) and the SIMO system is decomposed into a SISO system followed by a reduced SIMO system, as illustrated in Fig. 3. Obviously the order of these two subsystems does not affect the relationship between the input and outputs.

The particular positions of the loudspeaker will be specified when the measurements are used later on for algorithm evaluation. 2 Image Model for Acoustic Impulse Response Simulation Direct measurements of acoustic impulse responses are apparently ideal in the sense that they faithfully capture the characteristics of real-world acoustic channels. But the procedure is quite time consuming and the measurement facilities may be prohibitively expensive or may not be readily available. Consequently, a simple analytical model is desired for simulating acoustic impulse responses.

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