Algorithm 820: A flexible implementation of matching pursuit for Gabor functions on the interval
ACM Transactions on Mathematical Software (TOMS)
A high-resolution quadratic time-frequency distribution formulticomponent signals analysis
IEEE Transactions on Signal Processing
A fast refinement for adaptive Gaussian chirplet decomposition
IEEE Transactions on Signal Processing
Stochastic time-frequency dictionaries for matching pursuit
IEEE Transactions on Signal Processing
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It is well known that the convergence (with different speeds) of the matching pursuit (MP) signal decomposition algorithm for any dense dictionary is guaranteed. In this paper, we have analysed (in theory and through simulations) the performance and properties of both Gaussian and damped sinusoidal atoms for the MP signal decomposition. We have examined the decomposed signal in ambiguity space (to look for auto-terms concentrated around the origin), and investigated the requirement to have a positive time-frequency representation. We are thus able to propose what kind of dictionary might be more suitable for MP signal decomposition. We have also derived general formulae for the first and second conditional spectral moments, which are useful generalizations of the concept of instantaneous frequency and instantaneous bandwidth, respectively. While the second conditional moment is not positive for many bilinear time-frequency distributions, thus making useless its interpretation as instantaneous bandwidth, we have proved that for MP decomposition based on Gaussian or damped sinusoidal atoms, it is always guaranteed positive.