Geodesic
Composition of wavelet and Fourier transforms
Mathematica Applicanda, Tome 46 (2018) no. 1, pp. 159-168.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The paper presents the basic properties of the serial composition of two transformations: wavelet and Fourier. Two types of transformations were obtained because wavelet and Fourier transformations do not commute. The consequences of a phenomenon known as a "wavelet crime" are presented. Using wavelets with compact support in the frequency domain (e.g. Meyer wavelets) leads to the representation of signals as sparse matrices. Speech signals were used to test the presented transforms.
DOI : 10.14708/ma.v46i1.6376
Mots-clés : wavelet transform, Fourier transform, numerical methods, sparse systems 
@article{10_14708_ma_v46i1_6376,
     author = {Mariusz Zi\'o{\l}ko and Marcin Witkowski and Jakub Ga{\l}ka},
     title = {Composition of wavelet and {Fourier} transforms},
     journal = {Mathematica Applicanda},
     pages = { 159--168},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2018},
     doi = {10.14708/ma.v46i1.6376},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v46i1.6376/}
}
TY  - JOUR
AU  - Mariusz Ziółko
AU  - Marcin Witkowski
AU  - Jakub Gałka
TI  - Composition of wavelet and Fourier transforms
JO  - Mathematica Applicanda
PY  - 2018
SP  -  159
EP  - 168
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/ma.v46i1.6376/
DO  - 10.14708/ma.v46i1.6376
LA  - pl
ID  - 10_14708_ma_v46i1_6376
ER  - 
%0 Journal Article
%A Mariusz Ziółko
%A Marcin Witkowski
%A Jakub Gałka
%T Composition of wavelet and Fourier transforms
%J Mathematica Applicanda
%D 2018
%P  159-168
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/ma.v46i1.6376/
%R 10.14708/ma.v46i1.6376
%G pl
%F 10_14708_ma_v46i1_6376
Mariusz Ziółko; Marcin Witkowski; Jakub Gałka. Composition of wavelet and Fourier transforms. Mathematica Applicanda, Tome 46 (2018) no. 1, pp.  159-168. doi : 10.14708/ma.v46i1.6376. http://geodesic.mathdoc.fr/articles/10.14708/ma.v46i1.6376/

Cité par Sources :