8 The DUET Blind Source Separation

This chapter presents a tutorial on the DUET Blind Source Separation method which can separate any number of sources using only two mixtures. The method is valid when sources are W-disjoint orthogonal, that is, when the supports of the windowed Fourier transform of the signals in the mixture are disjoint. For anechoic mixtures of attenuated and delayed sources, the method allows one to estimate the mixing parameters by clustering relative attenuation-delay pairs extracted from the ratios of the time–frequency representations of the mixtures. The estimates of the mixing parameters are then used to partition the time–frequency representation of one mixture to recover the original sources. The technique is valid even in the case when the number of sources is larger than the number of mixtures. The method is particularly well suited to speech mixtures because the time–frequency representation of speech is sparse and this leads to W-disjoint orthogonality. The algorithm is easily coded and a simple Matlab implementation is presented. Additionally in this chapter, two strategies which allow DUET to be applied to situations where the microphones are far apart are presented; this removes a major limitation of the original method.