Non-stationary Multiscale Analysis

Orthonormal bases of wavelets and wavelet packets yield linear, non-redundant time-scale and time-frequency decompositions for arbitrary functions and signals. Numerically, these decompositions are based on the iterative application of digital filter banks. Usually these filters are the same at every iteration. We show here the advantages of using filters that may vary from one iteration to the next one. An appropriate choice leads to C∞ compactly supported wavelets and allows a better control of the time-frequency localization properties of wavelet packets. These results have been obtained jointly with N. Dyn of Tel-Aviv University and E. Séré of CEREMADE