A GENERALIZATION OF A CLASS OF BLIND SOURCE SEPARATION ALGORITHMS FOR CONVOLUTIVE MIXTURES

There are two main approaches for blind source separation (BSS) on time series using second-order statistics. One is to utilize the nonwhiteness property, and the other one is to utilize the nonstationarity property of the source signal. In this paper, we combine both approaches for convolutive mixtures using a matrix notation that leads to a number of new insights. We give rigorous derivations of the corresponding time-domain and frequency-domain approaches by generalizing a known cost function so that it inherently allows joint optimization for several time lags of the correlations. The approach is suitable for on-line and off-line algorithms by introducing a general weighting function allowing for tracking of time-varying environments. For both, the time-domain and frequency-domain versions, we discuss links to well-known and also to extended algorithms as special cases. Moreover, using the so-called generalized coherence, we establish links between the time-domain and frequency-domain algorithms and show that our cost function leads to an update equation with an inherent normalization.

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