Two new convolutions for the fractional Fourier transform

Detalhes bibliográficos
Autor(a) principal: Anh, P. K.
Data de Publicação: 2017
Outros Autores: Castro, L. P., Thao, P. T., Tuan, N. M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/16666
Resumo: In this paper we introduce two novel convolutions for the fractional Fourier transforms (FRFT), and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish a necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in L^1(R) and L^2(R) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper.
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spelling Two new convolutions for the fractional Fourier transformConvolutionConvolution theoremFractional Fourier transformConvolution equationFilteringIn this paper we introduce two novel convolutions for the fractional Fourier transforms (FRFT), and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish a necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in L^1(R) and L^2(R) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper.Springer Verlag2018-07-20T14:00:58Z2017-01-12T00:00:00Z2017-01-122018-01-12T19:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16666eng0929-621210.1007/s11277-016-3567-3Anh, P. K.Castro, L. P.Thao, P. T.Tuan, N. M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:31:15Zoai:ria.ua.pt:10773/16666Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:47.703172Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Two new convolutions for the fractional Fourier transform
title Two new convolutions for the fractional Fourier transform
spellingShingle Two new convolutions for the fractional Fourier transform
Anh, P. K.
Convolution
Convolution theorem
Fractional Fourier transform
Convolution equation
Filtering
title_short Two new convolutions for the fractional Fourier transform
title_full Two new convolutions for the fractional Fourier transform
title_fullStr Two new convolutions for the fractional Fourier transform
title_full_unstemmed Two new convolutions for the fractional Fourier transform
title_sort Two new convolutions for the fractional Fourier transform
author Anh, P. K.
author_facet Anh, P. K.
Castro, L. P.
Thao, P. T.
Tuan, N. M.
author_role author
author2 Castro, L. P.
Thao, P. T.
Tuan, N. M.
author2_role author
author
author
dc.contributor.author.fl_str_mv Anh, P. K.
Castro, L. P.
Thao, P. T.
Tuan, N. M.
dc.subject.por.fl_str_mv Convolution
Convolution theorem
Fractional Fourier transform
Convolution equation
Filtering
topic Convolution
Convolution theorem
Fractional Fourier transform
Convolution equation
Filtering
description In this paper we introduce two novel convolutions for the fractional Fourier transforms (FRFT), and prove natural algebraic properties of the corresponding multiplications such as commutativity, associativity and distributivity, which may be useful in signal processing and other types of applications. We analyze a consequent comparison with other known convolutions, and establish a necessary and sufficient conditions for the solvability of associated convolution equations of both the first and second kind in L^1(R) and L^2(R) spaces. An example satisfying the sufficient and necessary condition for the solvability of the equations is given at the end of the paper.
publishDate 2017
dc.date.none.fl_str_mv 2017-01-12T00:00:00Z
2017-01-12
2018-07-20T14:00:58Z
2018-01-12T19:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/16666
url http://hdl.handle.net/10773/16666
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0929-6212
10.1007/s11277-016-3567-3
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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