ON GENERALIZED-MARGINAL TIME-FREQUENCY DISTRIBUTIONS

In this correspondence, we introduce a family of time-frequency (TF) d istributions with generalized marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitu de squared of the fractional Fourier transforms of the signal. We pres ent a necessary and sufficient condition for a TF distribution in Cohe n's class to satisfy generalized marginals, We then modify the existin g a well-known TF distributions in Cohen's class, such as Choi-William s and Page distributions, so that the modified ones have generalized m arginals. Numerical examples are presented to show that the proposed T F distributions have the advantages of both Wigner-Ville and other qua dratic TF distributions, which only have the conventional marginal. Mo reover, they also indicate that the generalized-marginal TF distributi ons with proper marginals are more robust than the Wigner-Ville and th e Choi-Williams distributions when signals contain additive noises.