Wavelet windowed time-frequency distribution decompositions

William J. Williams; Tzuhsien Sang; Jeffrey C. O Neill; Eugene J. Zalubas

doi:10.1117/12.284184

24 October 1997 Wavelet windowed time-frequency distribution decompositions

William J. Williams, Tzuhsien Sang, Jeffrey C. O Neill, Eugene J. Zalubas

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.284184
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

This paper outlines means of combining and reconciling concepts associated with Cohen's class of distributions and with the wavelet transform. Both have their assets and their liabilities. Previous work has shown that one can decompose any time-frequency distribution (TFD) in Cohen's class into a weighted sum of spectrograms. A set of orthogonal analysis windows which also have the scaling property in common with wavelets is proposed. Successful application of this theory offers very fast computation of TFDs, since very few analysis windows may be needed and fast algorithms can be used. In addition, the decomposition idea offers the possibility of shaping the analysis such that good local and global properties as well as a number of desirable TFD properties are retained. Finally, one may view the result in terms of conventional Cohen's class concepts or, alternatively, in terms of wavelet concepts and potentially combine powerful insights and concepts from both points of view. Preliminary results applied to radar backscatter are provided. Performance curves for several wavelet types are also provided.

Citation Download Citation

William J. Williams, Tzuhsien Sang, Jeffrey C. O Neill, and Eugene J. Zalubas "Wavelet windowed time-frequency distribution decompositions", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.284184

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