Frequency localization of wavelet packets.

Eric Séré

Revista Matemática Iberoamericana (1995)

  • Volume: 11, Issue: 2, page 334-354
  • ISSN: 0213-2230

Abstract

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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-jΣn=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.

How to cite

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Séré, Eric. "Localisation fréquentielle des paquets d'ondelettes.." Revista Matemática Iberoamericana 11.2 (1995): 334-354. <http://eudml.org/doc/39475>.

@article{Séré1995,
author = {Séré, Eric},
journal = {Revista Matemática Iberoamericana},
keywords = {Tratamiento de señales; Función armónica; Algoritmos de filtro; Bases ortonormales; Paquetes; Ondículas; Filtro divisor frecuencias; wavelet packets; signal compression; frequency localization; dyadic expansion; filters},
language = {fre},
number = {2},
pages = {334-354},
title = {Localisation fréquentielle des paquets d'ondelettes.},
url = {http://eudml.org/doc/39475},
volume = {11},
year = {1995},
}

TY - JOUR
AU - Séré, Eric
TI - Localisation fréquentielle des paquets d'ondelettes.
JO - Revista Matemática Iberoamericana
PY - 1995
VL - 11
IS - 2
SP - 334
EP - 354
LA - fre
KW - Tratamiento de señales; Función armónica; Algoritmos de filtro; Bases ortonormales; Paquetes; Ondículas; Filtro divisor frecuencias; wavelet packets; signal compression; frequency localization; dyadic expansion; filters
UR - http://eudml.org/doc/39475
ER -

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