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Proceedings Paper

Wavelet windowed time-frequency distribution decompositions
Author(s): William J. Williams; Tzuhsien Sang; Jeffrey C. O Neill; Eugene J. Zalubas
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Paper 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.

Paper Details

Date Published: 24 October 1997
PDF: 12 pages
Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); doi: 10.1117/12.284184
Show Author Affiliations
William J. Williams, Univ. of Michigan (United States)
Tzuhsien Sang, Univ. of Michigan (United States)
Jeffrey C. O Neill, Univ. of Michigan (United States)
Eugene J. Zalubas, Univ. of Michigan (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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