A new positive time-frequency distribution

This article studies the formulation of new members of the Cohen-Posch (1985) class of positive time-frequency energy distributions. Members of this class are always positive functionals and satisfy the marginal constraints. Therefore, they can be properly interpreted as distributions. We considered the minimization of cross-entropy measures with respect to different priors or “a priori” distributions and the case of no prior or maximum entropy, and concluded with the necessity to introduce new marginal constraints. New mixed in time and frequency constraints are derived based on a “direction invariance” criterion on the time-frequency plane that are directly related to the Fractional Fourier Transform. The implications of this new constrains in the positive class are analyzed from an information theoretic perspective. We conclude that the new constraints provide enough information to fully determine the resulting distribution and thus, no “a priori” distribution is necessary