On the decomposition of multichannel nonstationary multicomponent signals

Abstract

With their ability to cater for simultaneously for multifaceted information, multichannel (multivariate) signals have been used to solve problems that are normally not solvable with signals obtained from a single source. One such problem is the decomposition of signals which comprise several components for which the domains of support significantly overlap in both the time, frequency and the joint time-frequency domain. Earlier, we proposed a solution to this problem based on the Wigner distribution of multichannel signals, which requires the attenuation of the cross-terms. In this paper, an advanced solution is proposed, based on eigenvalue analysis of the multichannel signal autocorrelation matrix, followed by the minimization of their time-frequency concentration measure. The analysis offers less restrictive conditions for the signal decomposition, compared to the case of the Wigner distribution. The algorithm for the separation of components is based on concentration measures of the eigenvector time-frequency representation, which represent linear combinations of the overlapping signal components. With an increased number of sensors/channels, the robustness of the decomposition process to additive noise is also demonstrated. The theory is supported by numerical examples, whereby the required channel dissimilarity is also statistically investigated.