Some simple parameter determination rules for the generalized Choi-Williams and Butterworth distributions

Papandreou and Boudreaux-Bartels (1992, 1993) proposed two new elements of the Cohen's class. The interesting point of these time-frequency distributions is their characteristic kernels, which differ from the product type kernels in an included dissymmetry between the Doppler and lag variables. Together with these definitions, a parameter determination scheme was proposed, which requires one to compute the ambiguity function of the analyzed signal and to discriminate there the cross-terms from the signal components. The aim of the present paper is to deduce from the cross-term reduction mechanism of these distributions a simple parameter determination rule, which requires less knowledge on the signal structure. The author also defines and studies a new distribution which is the asymptotic limit of both these distributions as their order increases.<>