Evolutionary chirp representation of non-stationary signals via Gabor transform

In this paper, we propose a chirp time-frequency representation for non-sta tionary signals, and associate with it-via a multi-window Gabor expansion-t he 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 bandw idth 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 r esolutions is obtained from the kernel of the representation. The chirp rep resentation optimally chooses scales and linear chirp slopes by maximizing a local energy concentration measure. Parsimonious signal representation an d well-localized evolutionary spectrum are obtained simultaneously. As an a pplication of our representation, we consider the excision of broad-band ja mmers in spread spectrum communications. Examples illustrating the improvem ent in the time and frequency resolution of the signal spectrum using our p rocedure are given. (C) 2001 Elsevier Science B.V. All rights reserved.