Positive Time - Frequency Distributions via Maximum Entropy Deconvolution of the Evolutionary Spectrum

This material is posted here with permission of the IEEE. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by sending a blank email message to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Abstract The relationship between Priestley's definition of the evolutionary spectrum (ES) and the Cohen-Posch class of positive time-frequency energy 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 nor-malization 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.