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Proceedings Paper

Algorithm for weighted least squares positive time-frequency distributions
Author(s): James W. Pitton
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Paper Abstract

An algorithm for computing positive time-frequency distributions (TFDs) for nonstationary signals is presented. This work extends the earlier work of the author and his colleagues in computing positive TFDs. A general approach to the problem of computing these signal-dependent distributions is derived. The method is based on an evolutionary spectrum formulation of positive TFDs. Following earlier work, a relationship is derived between positive TFDs and the ambiguity function of the observed signal. In particular, it is shown that the TFD is approximately equal to the two-dimensional Fourier transform of the ambiguity function. A method for computing the positive TFD is then presented based on minimizing the squared error in this approximation subject to the TFD being positive and satisfying the time and frequency marginals. The squared error may be weighted non-uniformly, resulting on a constrained weighted least-squares optimization problem. A solution to this optimization problem based on an alternating projections framework is presented, and an example is provided. The resulting TFD provides excellent time-frequency resolution while maintaining positivity and satisfying the marginals.

Paper Details

Date Published: 24 October 1997
PDF: 9 pages
Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); doi: 10.1117/12.284196
Show Author Affiliations
James W. Pitton, MathSoft (United States)

Published in SPIE Proceedings Vol. 3162:
Advanced Signal Processing: Algorithms, Architectures, and Implementations VII
Franklin T. Luk, Editor(s)

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