On the locus and spread of pseudo-density functions in the time-frequency plane

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Abstract

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.
Original languageEnglish
Pages (from-to)79-110
Number of pages17
JournalPhilips Journal of Research
Volume37
Issue number3
Publication statusPublished - 1982

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