Acoustic MIMO Signal Processing (2006) (Signals and by Yiteng Huang

By Yiteng Huang

Telecommunication structures and human-machine interfaces have all started utilizing a number of microphones and loudspeakers to render interplay extra realistic, and extra effective. This increases acoustic sign processing difficulties below 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, and so forth. The ebook opens with an acoustic MIMO paradigm, developing basics, and linking acoustic MIMO sign processing with classical sign processing and communique theories. the second one a part of the booklet provides a unique research of acoustic functions performed within the paradigm to augment the basics of acoustic MIMO sign processing.

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19) /3—*oo While the Dirac filter is the sparest of all possible impulse responses, the uniform filter is the densest or least sparse one. The filter he is a good model of acoustic impulse responses where 0 depends on the reverberation time. For a long reverberation time (large /5), he will decay slowly while for a short reverberation time (small P) he will decay rapidly. 3 Measurement and Simulation of MIMO Acoustic Systems (a) (b) (c) (d) 0 < ,e(h) < 1, VaT^O, a « h ) = e(h), e(hd) = 1, ^(hu) = 0.

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).

Therefore, a stable, causal system has a stable and causal inverse only if both its poles and zeros are inside the unit circle. Such a system is commonly referred to as a minimum-phase system. Minimum-phase systems have the properties of minimum phase-lag, minimum group delay, and minimum energy delay. Therefore a more precise terminology is minimum phase-lag, minimum group-delay, or minimum energy-delay system, but none of these is widely used and "minimum phase is historically the established terminology" [244].

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