On the convergence of derivatives of B-splines to derivatives of the Gaussian function

Detalhes bibliográficos
Autor(a) principal: Brinks,Ralph
Data de Publicação: 2008
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000100005
Resumo: In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in the continuous wavelet transform (CWT) of a function analyzed with different B-spline wavelets.
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spelling On the convergence of derivatives of B-splines to derivatives of the Gaussian functionB-splinesGaussian functionContinuous wavelet transformMexican hat waveletScalogramIn 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in the continuous wavelet transform (CWT) of a function analyzed with different B-spline wavelets.Sociedade Brasileira de Matemática Aplicada e Computacional2008-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000100005Computational & Applied Mathematics v.27 n.1 2008reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMACinfo:eu-repo/semantics/openAccessBrinks,Ralpheng2008-04-02T00:00:00Zoai:scielo:S1807-03022008000100005Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2008-04-02T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv On the convergence of derivatives of B-splines to derivatives of the Gaussian function
title On the convergence of derivatives of B-splines to derivatives of the Gaussian function
spellingShingle On the convergence of derivatives of B-splines to derivatives of the Gaussian function
Brinks,Ralph
B-splines
Gaussian function
Continuous wavelet transform
Mexican hat wavelet
Scalogram
title_short On the convergence of derivatives of B-splines to derivatives of the Gaussian function
title_full On the convergence of derivatives of B-splines to derivatives of the Gaussian function
title_fullStr On the convergence of derivatives of B-splines to derivatives of the Gaussian function
title_full_unstemmed On the convergence of derivatives of B-splines to derivatives of the Gaussian function
title_sort On the convergence of derivatives of B-splines to derivatives of the Gaussian function
author Brinks,Ralph
author_facet Brinks,Ralph
author_role author
dc.contributor.author.fl_str_mv Brinks,Ralph
dc.subject.por.fl_str_mv B-splines
Gaussian function
Continuous wavelet transform
Mexican hat wavelet
Scalogram
topic B-splines
Gaussian function
Continuous wavelet transform
Mexican hat wavelet
Scalogram
description In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in the continuous wavelet transform (CWT) of a function analyzed with different B-spline wavelets.
publishDate 2008
dc.date.none.fl_str_mv 2008-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000100005
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022008000100005
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
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 Computational & Applied Mathematics v.27 n.1 2008
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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