Conditional Non-Central Moments and Characteristic Function Based on Matching Pursuit

In this paper, we decompose a non-stationary signal by use of the matching pursuit (MP) algorithm through using two different types of dictionaries (i.e., the Gaussian and chirplet dictionaries). Then we give expressions for the first and second-order conditional spectral moments, which are generalizations of the ideas of instantaneous frequency and instantaneous bandwidth. Although in many cases the second-order conditional spectral moment is not positive and this makes the usual interpretation of this quantity impossible, with MP decomposition, by using the Gaussian or chirplet dictionaries, the second-order conditional spectral moment is always positive. In addition, we derive the characteristic function for the MP distribution. So the joint higher-order statistical moments can be calculated by differentiation simply. We also analyze a bat sound signal with short time Fourier transform (STFT) as well as the adaptive signal decomposition, MP, and compare the resolution of relative time-frequency distributions

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