Fixed and data adaptive kernels in Cohen's class of time-frequency distributions

Abstract

Estimating the spectra of non-stationary signals represents a difficult challenge. Classical techniques employing the Fourier transform and local stationarity have been employed with limited success. A more promising approach is the use of time-frequency distributions. The majority of useful distributions have been unified under Cohen's class of distributions, a bilinear transformation with an arbitrary, fixed kernel function. The properties of several popular distributions developed from Cohen's class of distribution are examined. the ability of the kernel to suppress spurious cross-terms resulting from the bilinear nature of these distributions is examined along with their characteristics. Distributions employing a fixed kernel usually give good results only for a small class of signals. A data adaptive kernel is also examined which promises to give superior results for a broad class of signals. Results are shown for several test cases employing synthetic, analytic signals.