Adaptive time-frequency transform

A matching pursuit decomposes any signal into a linear expansion of waveforms that belong to a dictionary of functions. These waveforms are selected in order to best match the signal structures. For dictionaries of functions that have a wide range of different time-frequency localizations, a matching pursuit yields an adaptive time-frequency transform. The authors derive a signal energy distribution in the time-frequency plane which does not include interference terms, unlike Wigner and Cohen class distributions. Signal components that are coherent with respect to the dictionary can be extracted. It is shown that time-frequency dictionaries yield adaptive decompositions where signal structures are represented by Gabor functions that match their time-frequency signature. The properties of the signal components are explicitly given by the scale, frequency, time, and phase indexes of the selected Gabor functions.<>