Comparing Gaussian and chirplet dictionaries for time-frequency analysis using matching pursuit decomposition

Abstract

As convergence of the matching pursuit (MP) decomposition is not dependent upon the type of atom used, we are free to assume different dictionaries. In this paper we compare the chirplet and Gaussian atoms, because both always give positive values for the Wigner-Ville distribution, and therefore the MP distribution is also always positive (as mathematically required). We show that when the MP decomposition is applied to analyze a time-varying signal, the chirplet atom is better than the Gaussian atom in tracking the instantaneous frequency. Although computational more demanding, we see that it also has a faster convergence rate. Finally, the resolution of the extracted MP distribution with the chirplet atom can also be clearly observed to be superior.