Blind Source Separation Of Convolutive Mixtures

Blind source separation is a technology that can recover the sources signal only according to several sensor signals from unknown mixing system. In early studies, since not considering the effects of delayed and filtered when signal transmitted we got lots of classical methods for linear instantaneous mixtures, such as the mutual minimization, FastICA, Natural Gradient and Relative Gradient. However, these algorithms are disabled when they are used to the real signals which often are convolutive mixtures in time domain.Relative to blind source separation of instantaneous mixtures, the blind source separation of convolutive mixtures is more complicated. In recent years, many algorithms for blind source separation of convolutive mixtures are developed. For blind source separation of convolutive mixture, there are two types of approach. One is a time-domain approach, and the other is a frequency-domain one. Many of the algorithms in the time domain are obtained by extended the algorithms for the blind source separation of instantaneous mixtures from translating the convolutive mixtures to the form of the instantaneous mixtures or modifying the cost function of blind source separation of instantaneous mixtures. However, the rate of convergence of the algorithms in time domain is very slow when the length of the mixing filter is long. In the frequency-domain approach, the observed signals are first converted to time frequency signals by applying Fourier transform to block wisely segmented data. Then, independent components for each frequency range are extracted. This approach has two serious problems which are inherent in BSS: the permutation and scale problem. To reconstruct the source signals from the frequency-domain data, we have to align the problems for all the frequency components. To eliminate those indeterminacies, some complex calculation is usually required. At the same time, the translations in signal domain bring some non- neglectable influences to the hypothesis of the independence.There are many potential applications for blind source separation of convolutive mixtures, especially in communication, medical signal processing, speech processing and underwater acoustics. Blind source separation of convolutive mixtures is one of the top fields of the research of blind source separation. In this thesis, the algorithm of blind source separation of convolutive mixtures in time domain has been studied based on the detailed discussion of its theory.This dissertation consists of five chapters.In chapter one, we introduce the historical perspective of blind source separation of convolutive mixtures.In chapter two, first, we explain the mathematics models of blind source separation. Then introduce the foundation mathematics theory of blind source separation of convolutive mixtures, including discrete time filters, z transform and matrix theory. We discuss the indeterminacies and introduce two measures of the separation performance. Finally, we present three classical algorithms.In chapter three, we introduce an algorithm of whitening firstly. We propose a nonlinear principle component analysis (PCA) cost function for blind separation of convolutive mixtures. Then a new recursive least-squares (RLS) algorithm is developed in time domain. Simulations show that our algorithm can successfully separate convolutive mixtures and has fast convergence.In chapter four, we introduce regulation owning to the regulation allow of some error. Then we get a novel cost function, by minimizing the cost function we get a new recursive least-squares (RLS) algorithm. Simulations show that our algorithm can successfully separate convolutive mixtures and has fast convergence, and the performance is better that of the algorithm in chapter three.In chapter five, we conclude the research and present our further research.