Blind Source Separation of Convolved Sources by Joint Approximate Diagonalization of Cross-Spectral Density Matrices

In this paper we present a new method for separating non-stationary sources from their convolutive mixtures based on approximate joint diagonalization of the observed signals' cross-spectral density matrices. Several blind source separation (BSS) algorithms have been proposed which use approximate joint diagonalization of a set of scalar matrices to estimate the instantaneous mixing matrix. We extend the concept of approximate joint diagonalization to estimate MIMO FIR channels. Based on this estimate we then design a separating network which will recover the original sources up to only a permutation and scaling ambiguity for minimum phase channels. We eliminate the commonly experienced problem of arbitrary scaling and permutation at each frequency bin, by optimizing the cost function directly with respect to the time-domain channel variables. We demonstrate the performance of the algorithm by computer simulations using real speech data. Speech samples are available at: http://sparky.mcmaster.ca/SSP/telephony_kamran.htm.