Localisation fréquentielle des paquets d'ondelettes
- Autores: Eric Séré
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 11, Nº 2, 1995, págs. 334-354
- Idioma: francés
- DOI: 10.4171/rmi/175
- Títulos paralelos:
- Localización frecuencial de los paquetes de ondículas
- Frequency localization of wavelet packets.
- Enlaces
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Resumen
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.
