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 suffer a lack of frequency localization. Using the -norm of the Fourier transform as localization criterion, they showed that the average blows up as goes to infinity. A natural problem is then to know which values of create this blowup in average. The present work gives an answer to this question thanks to sharp estimates on which depend on the dyadic expansion of for several types of filters. Let us point out that the value of is a weak localization criterion, which can only lead to a lower estimate on the variance of .
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Éric Séré, Localisation fréquentielle des paquets d'ondelettes. Rev. Mat. Iberoam. 11 (1995), no. 2, pp. 334–354DOI 10.4171/RMI/175