A centrosymmetric kernel decomposition for time-frequency distribution computation

Authors:
S. Aviyente;W.J. Williams
Affiliations:
Dept. of Electr. & Comput. Eng., Michigan State Univ., East Lansing, MI, USA;-
Venue:
IEEE Transactions on Signal Processing
Year:
2004

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Abstract

Time-frequency distributions (TFDs) are bilinear transforms of the signal and, as such, suffer from a high computational complexity. Previous work has shown that one can decompose any TFD in Cohen's class into a weighted sum of spectrograms. This is accomplished by decomposing the kernel of the distribution in terms of an orthogonal set of windows. In this paper, we introduce a mathematical framework for kernel decomposition such that the windows in the decomposition algorithm are not arbitrary and that the resulting decomposition provides a fast algorithm to compute TFDs. Using the centrosymmetric structure of the time-frequency kernels, we introduce a decomposition algorithm such that any TFD associated with a bounded kernel can be written as a weighted sum of cross-spectrograms. The decomposition for several different discrete-time kernels are given, and the performance of the approximation algorithm is illustrated for different types of signals.