A signal-adaptive time-frequency distribution using generalized marginals

Abstract

The joint time-frequency distributions are widely used in the analysis of non-stationary signals. These distributions are bilinear with respect to the signal, thereby producing cross-terms which are detrimental to an intuitive understanding of the distribution. All the time-frequency distributions designed for the purpose of suppressing cross-terms have lowpass smoothing kernels designed in the ambiguity domain. We introduce a signal-adaptive kernel designed in the generalized marginals (GM) domain. This new kernel exploits the mechanism by which the cross-terms are created in the GM domain. It is shown that the cross-terms are created by a simple squaring process and the region of support for the cross terms is a subset of the region of support of the auto-terms. The generalized marginals of the Wigner distribution (WD) are always positive and real. The generalized marginals of all distributions-which have a radially Gaussian kernel in the ambiguity domain are positive. This positivity is exploited for applying information measures in the construction of the adaptive kernel. The cross-term suppression is done in the GM domain and the time-frequency distribution is constructed using the filtered back-projection method. Moyal's formula is utilized to calculate the GM as the projections of the signal on linear chirps. >