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Proceedings Paper

Construction of time-frequency representations from moments
Author(s): Leon Cohen; Patrick Loughlin; Keith Davidson
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Paper Abstract

Given the moments of a time-frequency distribution, one can, in principle, construct the characteristic function from which one then obtains the distribution by Fourier transformation. However, often one can not find a closed form for the characteristic function and hence one can not obtain the distribution in a direct manner. We formulate the problem of constructing time-frequency representations from moments without first constructing the characteristic function. Our method is based on expanding the distribution in terms of a complete set of functions where the expansion coeficients are dependent directly on the moments. We apply the method to a case where the even moments are manifestly positive which is a necessary condition for obtaining a proper time-frequency representation.

Paper Details

Date Published: 25 September 2007
PDF: 8 pages
Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 66970B (25 September 2007); doi: 10.1117/12.740191
Show Author Affiliations
Leon Cohen, City Univ. of New York (United States)
Patrick Loughlin, Univ. of Pittsburgh (United States)
Keith Davidson, Office of Naval Research (United States)

Published in SPIE Proceedings Vol. 6697:
Advanced Signal Processing Algorithms, Architectures, and Implementations XVII
Franklin T. Luk, Editor(s)

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