On conditional spectral moments of Gaussian and damped sinusoidal atoms in adaptive signal decomposition

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. © 2005 Elsevier B.V. All rights reserved.