Positive time-frequency distributions via maximum entropy deconvolution of the evolutionary spectrum

The relationship between Priestley´s definition of the evolutionary densities (TFDs) is explored, and a synthesis method is presented. As defined by Priestley, the ES is not a member of the Cohen-Posch class of TFDs. However, it is shown that by choosing a unit-energy normalization for the envelope function of Priestley´s formulation, the energetic ES thus obtained is a member of the Cohen-Posch class of TFDs; this normalization differs from that chosen by Priestley. A method is then presented to obtain an estimate of the energetic ES. This method employs maximum entropy deconvolution of the spectrogram, which is itself a blurred version of the ES. Because the energetic ES is everywhere nonnegative and yields the correct marginal densities, it is a legitimate, joint time-frequency energy density of the signal, unlike the Wigner and other bilinear distributions that go negative.<>