Composition of wavelet and Fourier transforms

Mariusz Ziółko, Marcin Witkowski, and Jakub Gałka. "Composition of wavelet and Fourier transforms." Mathematica Applicanda 46.1 (2018): null. <http://eudml.org/doc/292907>.

@article{MariuszZiółko2018,
abstract = {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.},
author = {Mariusz Ziółko, Marcin Witkowski, Jakub Gałka},
journal = {Mathematica Applicanda},
keywords = {wavelet transform, Fourier transform, numerical methods, sparse systems},
language = {eng},
number = {1},
pages = {null},
title = {Composition of wavelet and Fourier transforms},
url = {http://eudml.org/doc/292907},
volume = {46},
year = {2018},
}

TY - JOUR
AU - Mariusz Ziółko
AU - Marcin Witkowski
AU - Jakub Gałka
TI - Composition of wavelet and Fourier transforms
JO - Mathematica Applicanda
PY - 2018
VL - 46
IS - 1
SP - null
AB - 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.
LA - eng
KW - wavelet transform, Fourier transform, numerical methods, sparse systems
UR - http://eudml.org/doc/292907
ER -