On alternative wavelet reconstruction formula: a case study of approximate wavelets
The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, whi...
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The Royal Society
2014-01-01
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Online Access: | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140124 |
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doaj-4b408003d7c04e8d9784a4d06e88932f2020-11-25T04:08:29ZengThe Royal SocietyRoyal Society Open Science2054-57032014-01-011210.1098/rsos.140124140124On alternative wavelet reconstruction formula: a case study of approximate waveletsElena A. LebedevaEugene B. PostnikovThe application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140124wavelet transformgaussian functionmorlet waveletreconstruction formulaadmissibility conditionhilbert transform |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Elena A. Lebedeva Eugene B. Postnikov |
spellingShingle |
Elena A. Lebedeva Eugene B. Postnikov On alternative wavelet reconstruction formula: a case study of approximate wavelets Royal Society Open Science wavelet transform gaussian function morlet wavelet reconstruction formula admissibility condition hilbert transform |
author_facet |
Elena A. Lebedeva Eugene B. Postnikov |
author_sort |
Elena A. Lebedeva |
title |
On alternative wavelet reconstruction formula: a case study of approximate wavelets |
title_short |
On alternative wavelet reconstruction formula: a case study of approximate wavelets |
title_full |
On alternative wavelet reconstruction formula: a case study of approximate wavelets |
title_fullStr |
On alternative wavelet reconstruction formula: a case study of approximate wavelets |
title_full_unstemmed |
On alternative wavelet reconstruction formula: a case study of approximate wavelets |
title_sort |
on alternative wavelet reconstruction formula: a case study of approximate wavelets |
publisher |
The Royal Society |
series |
Royal Society Open Science |
issn |
2054-5703 |
publishDate |
2014-01-01 |
description |
The application of the continuous wavelet transform to the study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies owing to the admissibility condition. We propose an alternative reconstruction formula for the continuous wavelet transform, which is applicable even if the admissibility condition is violated. The case of the transform with the standard reduced Morlet wavelet, which is an important example of such analysing functions, is discussed. |
topic |
wavelet transform gaussian function morlet wavelet reconstruction formula admissibility condition hilbert transform |
url |
https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.140124 |
work_keys_str_mv |
AT elenaalebedeva onalternativewaveletreconstructionformulaacasestudyofapproximatewavelets AT eugenebpostnikov onalternativewaveletreconstructionformulaacasestudyofapproximatewavelets |
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