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Deep Sea Research Part B Oceanographic Literature Review

Positive time-frequency distribution functions [for formulating signal theory]

Published Jan 1, 1985• 0 citations
Publisher
DOI
10.1016/0198-0254(85)93005-5

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Cohen's (see Prentice Hall, Englewood Cliffs, NJ, 1995) class of time-frequency distributions for continuous signals has been to extended to discrete signals using both an axiomatic approach and an operator theory approach. We investigate the formulation of several classical time-frequency distributions (Wigner, Rihaczek, Margenau-Hill, Page, Levin, Born-Jordan, spectrogram) in the discrete Cohen's classes. The main result of this paper concludes that there does not exist a formulation of the Wigner distribution in all of the discrete Cohen's classes.

IEEE International Conference on Acoustics Speech and Signal Processing•Nov 27, 2002•3 citations
Various time-frequency pseudo-density functions used in signal analysis are compared with respect to spread. Among the members of Cohen's class of pseudo-density functions satisfying the finite support property as well as Moyal's formula, the Wigner distribution is the most well-behaved one in the sense that it has the least amount of global spread around its center of gravity. The Wigner distribution does not perform significantly better globally than the real part of Rihaczek's function; it does, though, if the global criterion is replaced by a local one, especially for signals f of the form f(t) equals a(t)exp(2 pi i phi (t)) where phi is a smooth real-valued function and a is a slowly varying positive function. A general principle is formulated according to which the various pseudo-density functions of f should be concentrated around the curve (t, phi prime (t)). A more detailed qualitative analysis of the behavior of the Wigner distribution of f around this curve is included.
Cohen's (see Prentice Hall, Englewood Cliffs, NJ, 1995) class of time-frequency distributions for continuous signals has been to extended to discrete signals using both an axiomatic approach and an operator theory approach. We investigate the formulation of several classical time-frequency distributions (Wigner, Rihaczek, Margenau-Hill, Page, Levin, Born-Jordan, spectrogram) in the discrete Cohen's classes. The main result of this paper concludes that there does not exist a formulation of the Wigner distribution in all of the discrete Cohen's classes.