A Simplified Frequency-domain Approach for Blind Separation of Convolutive Mixtures

In the frequency-domain, a convolutive mixture can be interpreted as several instantaneous mixtures which may be separated using many existing algorithms. The main limitation of this approach is the large number of frequencies that must be considered. In addition, a permutation/amplitude correction must be performed when the sources are recovered in a different order or with different amplitudes in some frequency bins. In this paper we propose a novel approach for solving the convolutive problem using only two frequency bins. The idea deals with finding a invertible matrix which relates the signals recovered in these frequency bins and the temporal sources. The existence of this matrix is due to use zeropadding for computing the Fourier transform of the observations. Several simulation results show the good performance of this simplified approach in different applications.