Signal separation - II

Abstract

Signal separation is a signal processing technique which enables the separation of superimposed signals. There are several practical situations were signal separation can be used, for example in noise reduction for cellular phones subject to background noise. The present thesis contains an overview of the signal separation topic along with papers on the subject. The included papers are to a large extent concerned with the two-input two-output case. However, the more general multi-input multi-output case is also treated. There are several techniques for deriving algorithms for signal separation. The present thesis exploits three techniques; 1) an ad-hoc system of difference equations; 2) criterion based optimization; 3) solving a system of non-linear equations. In the present thesis, second order statistics is mainly used. It is shown that second order statistics suffice for dynamical signal separation. In several instances it is verified that the problem at hand is parameter identifiable for large classes of channel systems using second order statistics. Furthermore, it is shown that the estimates are consistent given certain conditions. The local convergence to the solution representing separation is also treated. The local convergence analysis reveals that local convergence is linked to; 1) positive realness; 2) channel systems with a linear phase determinant. The performance of the presented algorithms can be evaluated using the Cramer-Rao lower bound. This bound is derived for the multi-input multi-output problem. Online monitoring can also be used to verify the performance of a signal separation algorithm. Two such monitoring schemes are derived based on the mutual information and the χ2-test.