Translational averaging for completeness, characterization and oversampling of wavelets.

Richard S. Laugesen

Collectanea Mathematica (2002)

  • Volume: 53, Issue: 3, page 211-249
  • ISSN: 0010-0757

Abstract

top
The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.

How to cite

top

Laugesen, Richard S.. "Translational averaging for completeness, characterization and oversampling of wavelets.." Collectanea Mathematica 53.3 (2002): 211-249. <http://eudml.org/doc/42924>.

@article{Laugesen2002,
abstract = {The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.},
author = {Laugesen, Richard S.},
journal = {Collectanea Mathematica},
keywords = {Ondículas; Completitud; Análisis de Fourier; Marcos de ondículas; Sobremuestreo; orthonormal wavelet; tight frame; oversampling; dual frame},
language = {eng},
number = {3},
pages = {211-249},
title = {Translational averaging for completeness, characterization and oversampling of wavelets.},
url = {http://eudml.org/doc/42924},
volume = {53},
year = {2002},
}

TY - JOUR
AU - Laugesen, Richard S.
TI - Translational averaging for completeness, characterization and oversampling of wavelets.
JO - Collectanea Mathematica
PY - 2002
VL - 53
IS - 3
SP - 211
EP - 249
AB - The single underlying method of averaging the wavelet functional over translates yields first a new completeness criterion for orthonormal wavelet systems, and then a unified treatment of known results on characterization of wavelets on the Fourier transform side, on preservation of frame bounds by oversampling, and on equivalence of affine and quasiaffine frames. The method applies to multiwavelet systems in all dimensions, to dilation matrices that are in some cases not expanding, and to dual frame pairs.
LA - eng
KW - Ondículas; Completitud; Análisis de Fourier; Marcos de ondículas; Sobremuestreo; orthonormal wavelet; tight frame; oversampling; dual frame
UR - http://eudml.org/doc/42924
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.