Evolutionary spectral analysis using a warped Gabor expansion

Abstract

In this paper, we present a Gabor representation based on a nonrectangular tiling of the time-frequency plane and use it to improve the time and frequency resolutions of evolutionary spectra. In the traditional Gabor expansion, a signal is decomposed into a weighted combination of sinusoidally modulated windows resulting in a rectangular time-frequency plane tiling. Poor time and frequency localizations occur in the evolutionary spectrum when the corresponding signal is not modeled well by this fixed-window analysis. We are thus proposing the warped Gabor representation based on a linear chirp model for the signal. By means of a frequency transformation we are able to use the previous sinusoidal representation and choose the Gabor coefficients according to either a frequency masking or an energy concentration measure. Examples are given to illustrate our procedures.