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

Authors:
J. W. Pitton;P. J. Loughlin;L. E. Atlas
Affiliations:
Dept. of Electr. Eng., Washington Univ., Seattle, WA, USA;Dept. of Electr. Eng., Washington Univ., Seattle, WA, USA;Dept. of Electr. Eng., Washington Univ., Seattle, WA, USA
Venue:
ICASSP '93 Proceedings of the Acoustics, Speech, and Signal Processing, 1993. ICASSP-93 Vol 4., 1993 IEEE International Conference on - Volume 04
Year:
1993

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Abstract

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.