Evolutionary chirp representation of non-stationary signals via Gabor transform

Abstract

In this paper, we propose a chirp time–frequency representation for non-stationary signals, and associate with it—via a multi-window Gabor expansion—the corresponding evolutionary spectra. Representations based on rectangular time–frequency plane tilings give poor time and frequency localization in the spectrum, especially when the signal is not modeled well by fixed bandwidth analysis. We propose a representation that uses scaled and translated windows modulated by chirps as bases. Considering a chirp-based Wold–Cramer model, the signal evolutionary spectrum with improved time and frequency resolutions is obtained from the kernel of the representation. The chirp representation optimally chooses scales and linear chirp slopes by maximizing a local energy concentration measure. Parsimonious signal representation and well-localized evolutionary spectrum are obtained simultaneously. As an application of our representation, we consider the excision of broad-band jammers in spread spectrum communications. Examples illustrating the improvement in the time and frequency resolution of the signal spectrum using our procedure are given.