Resumen de Localisation fréquentielle des paquets d'ondelettes

Eric Séré

• Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Koifman, Meyer and Wickerhauser that many wavelet packets wn suffer a lack of frequency localization. Using the L1-norm of the Fourier transform ^wn as localization criterion, they showed that the average 2-jSn=02j-1 ||^wn||L1 blows up as j goes to infinity. A natural problem is then to know which values of n create this blow-up in average. The present work gives an answer to this question, thanks to sharp estimates on ||^wn||L1 which depend on the dyadic expension of n, for several types of filters. Let us point out that the value of ||^wn||L1 is a weak localization criterion, which can only lead to a lower estimate on the variance of ^wn.