Weighted least squares implementation of Cohen-Posch time-frequency distributions

Abstract

We present an improvement of the least-squares method of Sang et al. (see Proc. IEEE-SP Int. Symp. Time-Freq./Time-Scale Anal., p.165-8, 1996) for constructing nonnegative joint time-frequency distributions (TFDs) satisfying the time and frequency marginals (i.e., Cohen-Posch (1985) distributions). The proposed technique is a positivity constrained iterative weighted least-squares (WLS) algorithm used to modify an initial TFD (e.g., any bilinear TFD) to obtain a Cohen-Posch TFD. The new algorithm solves the leakage problem of the least-squares approach and is computationaly faster. Examples illustrating the performance of the new algorithm are presented. The results for the WLS method compare favorably with the minimum cross-entropy method previously developed by Loughlin et al. (1992).