Adaptive kernel design in the generalized marginals domain for time-frequency analysis

A signal-adaptive kernel designed in the generalized marginals(GM) domain is introduced. 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