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SUMMARYIn correlation-based signal separation algorithms, the received mixed signals are fed to a de-coupling system designed to minimize the output cross-correlation functions. If minimizaion is perfect, each of the system's outputs carries only one signal independent of the others. In these algorithms, the computation burden of the output cross-correlation functions normally slows down the separation algorithm. This paper, describes a computationally e cient method for o -line pre-computation of the needed crosscorrelation functions. Explicit formulas have been derived for the output cross-correlation functions in terms of the received input signals and the de-coupling system parameters. Then, it is shown that signal separation amounts to the least-squares solution of a system of linear equations describing these output cross-correlation functions, evaluated over a batch of lags. Next, a fast RLS-type adaptive algorithm is devised for on-line signal separation. In this respect, an algorithm is derived for updating the de-coupling parameters as data comes in. This update is achieved recursively, along the negative of the steepest descent directions of an objective cost function describing the output cross-correlation functions over a batch of lags, subject to equal output power constraints. Illustrative examples are given to demonstrate the e ectiveness of the proposed algorithms.

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In this paper, a new approach based on the signal's time-frequency characterization, is described for blind source separation. Only two types of TFD algorithms are considered in signal separation applications, namely the short time Fourier transform STFT and Wigner-Ville distribution WVD. The main features of this approach apart from being suitable for non-stationary signals lie in the fact that it works satisfactorily even when the time-frequency signatures of the sources, overlap, or when the mixing system is convolutional and no longer linear. Illustrative examples are given to show that the proposed approach can successfully separate mixed signals when other approaches fail.