On generalized-marginal time-frequency distributions
We introduce a family of time-frequency (TF) distributions with generalized marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transfo...
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Published in | IEEE transactions on signal processing Vol. 44; no. 11; pp. 2882 - 2886 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
New York, NY
IEEE
01.11.1996
Institute of Electrical and Electronics Engineers |
Subjects | |
Online Access | Get full text |
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Summary: | We introduce a family of time-frequency (TF) distributions with generalized marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in Cohen's class to satisfy generalized marginals. We then modify the existing well-known TF distributions in Cohen's class, such as Choi-Williams (1989) and Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions, which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 1053-587X 1941-0476 |
DOI: | 10.1109/78.542448 |