A Centrosymmetric Kernel Decomposition for Time-Frequency Distribution Computation

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.