Two new convolutions for the fractional Fourier transform
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
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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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 |
format |
article |
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) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
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 |
repository.mail.fl_str_mv |
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1799137567787974656 |