Non-decimated Wavelet Transform for a Shift-invariant Analysis

Detalhes bibliográficos
Autor(a) principal: BRASSAROTE,G.O.N.
Data de Publicação: 2018
Outros Autores: SOUZA,E.M., MONICO,J.F.G.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100093
Resumo: ABSTRACT Due to the ability of time-frequency location, the wavelet transform has been applied in several areas of research involving signal analysis and processing, often replacing the conventional Fourier transform. The discrete wavelet transform has great application potential, being an important tool in signal compression, signal and image processing, smoothing and de-noising data. It also presents advantages over the continuous version because of its easy implementation, good computational performance and perfect reconstruction of the signal upon inversion. Nevertheless, the downsampling required in the computation of the discrete wavelet transform makes it shift variant and not appropriated to some applications, such as for signals or time series analysis. On the other hand, the Non-Decimated Discrete Wavelet Transform is shift-invariant because it eliminates the downsampling and, consequently, is more appropriate for identifying both stationary and non-stationary behaviors in signals. However, the non-decimated wavelet transform has been underused in the literature. This paper intends to show the advantages of using the non-decimated wavelet transform in signal analysis. The main theoretical and practical aspects of the multi-scale analysis of time series from non-decimated wavelets in terms of its formulation using the same pyramidal algorithm of the decimated wavelet transform was presented. Finally, applications with a simulated and real time series compare the performance of the decimated and non-decimated wavelet transform, demonstrating the superiority of non-decimated one, mainly due to the shift-invariant analysis, patterns detection and more perfect reconstruction of a signal.
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spelling Non-decimated Wavelet Transform for a Shift-invariant AnalysisNon-decimated waveletsshift invariancetime seriessignal analysisABSTRACT Due to the ability of time-frequency location, the wavelet transform has been applied in several areas of research involving signal analysis and processing, often replacing the conventional Fourier transform. The discrete wavelet transform has great application potential, being an important tool in signal compression, signal and image processing, smoothing and de-noising data. It also presents advantages over the continuous version because of its easy implementation, good computational performance and perfect reconstruction of the signal upon inversion. Nevertheless, the downsampling required in the computation of the discrete wavelet transform makes it shift variant and not appropriated to some applications, such as for signals or time series analysis. On the other hand, the Non-Decimated Discrete Wavelet Transform is shift-invariant because it eliminates the downsampling and, consequently, is more appropriate for identifying both stationary and non-stationary behaviors in signals. However, the non-decimated wavelet transform has been underused in the literature. This paper intends to show the advantages of using the non-decimated wavelet transform in signal analysis. The main theoretical and practical aspects of the multi-scale analysis of time series from non-decimated wavelets in terms of its formulation using the same pyramidal algorithm of the decimated wavelet transform was presented. Finally, applications with a simulated and real time series compare the performance of the decimated and non-decimated wavelet transform, demonstrating the superiority of non-decimated one, mainly due to the shift-invariant analysis, patterns detection and more perfect reconstruction of a signal.Sociedade Brasileira de Matemática Aplicada e Computacional2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512018000100093TEMA (São Carlos) v.19 n.1 2018reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2018.019.01.0093info:eu-repo/semantics/openAccessBRASSAROTE,G.O.N.SOUZA,E.M.MONICO,J.F.G.eng2018-05-24T00:00:00Zoai:scielo:S2179-84512018000100093Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-05-24T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Non-decimated Wavelet Transform for a Shift-invariant Analysis
title Non-decimated Wavelet Transform for a Shift-invariant Analysis
spellingShingle Non-decimated Wavelet Transform for a Shift-invariant Analysis
BRASSAROTE,G.O.N.
Non-decimated wavelets
shift invariance
time series
signal analysis
title_short Non-decimated Wavelet Transform for a Shift-invariant Analysis
title_full Non-decimated Wavelet Transform for a Shift-invariant Analysis
title_fullStr Non-decimated Wavelet Transform for a Shift-invariant Analysis
title_full_unstemmed Non-decimated Wavelet Transform for a Shift-invariant Analysis
title_sort Non-decimated Wavelet Transform for a Shift-invariant Analysis
author BRASSAROTE,G.O.N.
author_facet BRASSAROTE,G.O.N.
SOUZA,E.M.
MONICO,J.F.G.
author_role author
author2 SOUZA,E.M.
MONICO,J.F.G.
author2_role author
author
dc.contributor.author.fl_str_mv BRASSAROTE,G.O.N.
SOUZA,E.M.
MONICO,J.F.G.
dc.subject.por.fl_str_mv Non-decimated wavelets
shift invariance
time series
signal analysis
topic Non-decimated wavelets
shift invariance
time series
signal analysis
description ABSTRACT Due to the ability of time-frequency location, the wavelet transform has been applied in several areas of research involving signal analysis and processing, often replacing the conventional Fourier transform. The discrete wavelet transform has great application potential, being an important tool in signal compression, signal and image processing, smoothing and de-noising data. It also presents advantages over the continuous version because of its easy implementation, good computational performance and perfect reconstruction of the signal upon inversion. Nevertheless, the downsampling required in the computation of the discrete wavelet transform makes it shift variant and not appropriated to some applications, such as for signals or time series analysis. On the other hand, the Non-Decimated Discrete Wavelet Transform is shift-invariant because it eliminates the downsampling and, consequently, is more appropriate for identifying both stationary and non-stationary behaviors in signals. However, the non-decimated wavelet transform has been underused in the literature. This paper intends to show the advantages of using the non-decimated wavelet transform in signal analysis. The main theoretical and practical aspects of the multi-scale analysis of time series from non-decimated wavelets in terms of its formulation using the same pyramidal algorithm of the decimated wavelet transform was presented. Finally, applications with a simulated and real time series compare the performance of the decimated and non-decimated wavelet transform, demonstrating the superiority of non-decimated one, mainly due to the shift-invariant analysis, patterns detection and more perfect reconstruction of a signal.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01
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dc.language.iso.fl_str_mv eng
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dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.19 n.1 2018
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repository.mail.fl_str_mv castelo@icmc.usp.br
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