Wavelets obtained by continuous deformations of the Haar wavelet.

Bonami, Aline, Durand, Sylvain, and Weiss, Guido. "Wavelets obtained by continuous deformations of the Haar wavelet.." Revista Matemática Iberoamericana 12.1 (1996): 1-18. <http://eudml.org/doc/39516>.

@article{Bonami1996,
abstract = {One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show that any such wavelet can be connected in this way to the Haar wavelet.},
author = {Bonami, Aline, Durand, Sylvain, Weiss, Guido},
journal = {Revista Matemática Iberoamericana},
keywords = {Ondículas; Tratamiento de señales; Espacios de Frechet; Filtro paso-bajo; Transformada de Fourier; orthogonal wavelets; compactly supported; band-limited; Haar wavelet},
language = {eng},
number = {1},
pages = {1-18},
title = {Wavelets obtained by continuous deformations of the Haar wavelet.},
url = {http://eudml.org/doc/39516},
volume = {12},
year = {1996},
}

TY - JOUR
AU - Bonami, Aline
AU - Durand, Sylvain
AU - Weiss, Guido
TI - Wavelets obtained by continuous deformations of the Haar wavelet.
JO - Revista Matemática Iberoamericana
PY - 1996
VL - 12
IS - 1
SP - 1
EP - 18
AB - One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with reasonable (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show that any such wavelet can be connected in this way to the Haar wavelet.
LA - eng
KW - Ondículas; Tratamiento de señales; Espacios de Frechet; Filtro paso-bajo; Transformada de Fourier; orthogonal wavelets; compactly supported; band-limited; Haar wavelet
UR - http://eudml.org/doc/39516
ER -