Sparse signal representation with dispersion dictionary

Sparse decomposition of a signal can be obtained by decomposing signal in an overcomplete dictionary. The overcomplete dictionary function is generally all well-localized and well adapted to the signal's local structures. Although choosing an appropriate atom dictionary for analyses improves the performance of the analyses, modeling of the dispersion phenomenon will be necessary for accurate signal processing. In this paper, we introduce the dispersion dictionary which is an overcom-plete dictionary composed of Gaussian-envelop functions that can simulate the pulse dispersion phenomenon. The simulation result show the proposed dictionaries successfully represent nonstationary signals whose instantaneous frequency varies nonlineary with time and model the dispersion phenomenon. © Springer-Verlag Berlin Heidelberg 2011.