By Kostas Kokkinakis, Philipos C. Loizou

With human-computer interactions and hands-free communications turning into overwhelmingly very important within the new millennium, fresh examine efforts were more and more concentrating on cutting-edge multi-microphone sign processing suggestions to enhance speech intelligibility in opposed environments. One such admired statistical sign processing method is blind sign separation (BSS). This book investigates some of the most commercially appealing functions of BSS, that's the simultaneous restoration of indications inside of a reverberant (naturally echoing) atmosphere, utilizing (or extra) microphones. during this paradigm, each one microphone captures not just the direct contributions from each one resource, but additionally numerous mirrored copies of the unique indications at assorted propagation delays. those recordings are known as the convolutive combos of the unique assets. The aim of this e-book within the lecture sequence is to supply perception on fresh advances in algorithms, that are excellent for blind sign separation of convolutive speech combinations. extra importantly, particular emphasis is given in functional functions of the constructed BSS algorithms linked to real-life situations.

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INFORMATION-THEORETIC CRITERIA 25 with regards to the modus operandi of the entropy maximization method is provided in Torkkola (1999). Let us consider a signal passing through a bounded nonlinearity g(·), which is specifically chosen to model the cumulative densities of the sources. If we now assume that the network (or neuron) outputs denoted by u, correspond to the source estimates, then the resulting PDF will be close to a uniform density, that is a density which exhibits the largest entropy among all bounded distributions.

Throughout this section, we make the following assumptions: A1. At each time instant t, the components of the source vector s(t) are mutually statistically independent and therefore fulfill the condition E si (t) sj∗ (t − ) = 0, i = j and t = . A2. The original sources are zero-mean and second-order quasi-stationary signals and their autocorrelation function is independent of a time shift, such that Rs (t) = Rs (t + τ ) for some time constant τ = 0. A3. The number of sensors is equal to or greater than the number of the original sources, such that m n.

4. 24 2. MODERN BLIND SIGNAL SEPARATION ALGORITHMS the two sides of Eq. 5) as suggested by Comon (1994). , see Kullback, 1959). 2) i=1 Another interesting property of the KLD is that it is invariant with respect to any invertible linear transformation, including amplitude re-scaling and permutation re-ordering. 3) ENTROPY MAXIMIZATION Bell and Sejnowski (1995) were the first to frame BSS into an information-theoretic perspective. Their entropy (or information) maximization algorithm, known as INFOMAX, quickly catalyzed a surge of interest in using information theory for BSS.