Algorithm for weighted least squares positive time-frequency distributions

James W. Pitton

doi:10.1117/12.284196

24 October 1997 Algorithm for weighted least squares positive time-frequency distributions

James W. Pitton

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.284196
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

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.

Citation Download Citation

James W. Pitton "Algorithm for weighted least squares positive time-frequency distributions", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.284196

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