TIME-FREQUENCY REPRESENTATIONS - WAVELET PACKETS AND OPTIMAL DECOMPOSITION

We describe the construction of coherent states systems that do not generically come from a square integrable group representation. This property allows the construction of time-frequency representation theorems associated with arbitrary partitions of the Fourier space. As examples, we describe coherent states structures that interpolate between wavelets and Gabor functions, and others that have a wavelet behaviour at high frequencies, and a Gabor behaviour at low frequencies. A continuous analogue of the Coifman-Meyer-Wickerhauser minimal entropy criterion is proposed to select the optimal decomposition for a given analysed function.