A general framework for frequency domain multi-channel signal processing

In this paper, we provide a general framework for performing linear shift-invariant within channel and shift varying across channels processing of stationary multi-channel (MC) signals. Emphasis is given on the restoration of degraded signals. We show that, by utilizing the special structure of semi-block circulant and block diagonal matrices, MC signal processing can be easily carried out in the frequency domain. The generalization of many frequency domain single-channel (SC) signal processing techniques to the MC case is presented. We show that in MC signal processing each frequency component of a signal and system is respectively represented by a small vector and a matrix (of size equal to the number of channels), while in SC signal processing each frequency component in both cases is a scalar.