JournalsrmiVol. 11, No. 2pp. 334–354

Localisation fréquentielle des paquets d'ondelettes

  • Éric Séré

    Université de Paris Dauphine, France
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Abstract

Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Coifman, Meyer and Wickerhauser that "many" wavelet packets wnw_n suffer a lack of frequency localization. Using the L1L^1-norm of the Fourier transform w^n\hat{w}_n as localization criterion, they showed that the average 2jn=02j1w^nL12^{–j} \sum^{2^j–1}_{n=0} \|\hat{w}_n\|_{L^1} blows up as jj goes to infinity. A natural problem is then to know which values of nn create this blowup in average. The present work gives an answer to this question thanks to sharp estimates on w^nL1\|\hat{w}_n\|_{L^1} which depend on the dyadic expansion of nn for several types of filters. Let us point out that the value of w^nL1\|\hat{w}_n\|_{L^1} is a weak localization criterion, which can only lead to a lower estimate on the variance of w^n\hat{w}_n.

Cite this article

Éric Séré, Localisation fréquentielle des paquets d'ondelettes. Rev. Mat. Iberoam. 11 (1995), no. 2, pp. 334–354

DOI 10.4171/RMI/175