A method to detect and filter the cross terms in the Wigner-Ville distribution

Abstract

The Wigner-Ville distribution (WVD) is highly appreciated and used in the area of time-frequency transforms, but the problem of cross terms still remains. A simple idea is presented, as starting point to design a method to remove the cross terms and to obtain an accurate image of WVD, having only the auto terms. The idea uses the fact that the extreme (lateral) terms from WVD are always auto terms and a change in an auto term generates a change in at least one cross term. The identification of the auto terms is based on Renyi entropy, computed on the rows and columns of the WVD matrix, which has a minimum value for auto terms. An iterative method is next considered, which filter a component at each processing step. Finally, a WVD is obtained with auto terms only. The method is designed for non-overlapping multicomponent signals, without modulation. The results are promising.