A new convolution operator for the linear canonical transform with applications

Detalhes bibliográficos
Autor(a) principal: Castro, Luís P.
Data de Publicação: 2021
Outros Autores: Goel, Navdeep, Silva, Anabela S.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/31162
Resumo: The linear canonical transform plays an important role in engineering and many applied fields, as it is the case of optics and signal processing. In this paper, a new convolution for the linear canonical transform is proposed and a corresponding product theorem is deduced. It is also proved a generalized Young's inequality for the introduced convolution operator. Moreover, necessary and sufficient conditions are obtained for the solvability of a class of convolution type integral equations associated with the linear canonical transform. Finally, the obtained results are implemented in multiplicative filters design, through the product in both the linear canonical transform domain and the time domain, where specific computations and comparisons are exposed.
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spelling A new convolution operator for the linear canonical transform with applicationsLinear canonical transformConvolutionIntegral equationsFilteringThe linear canonical transform plays an important role in engineering and many applied fields, as it is the case of optics and signal processing. In this paper, a new convolution for the linear canonical transform is proposed and a corresponding product theorem is deduced. It is also proved a generalized Young's inequality for the introduced convolution operator. Moreover, necessary and sufficient conditions are obtained for the solvability of a class of convolution type integral equations associated with the linear canonical transform. Finally, the obtained results are implemented in multiplicative filters design, through the product in both the linear canonical transform domain and the time domain, where specific computations and comparisons are exposed.Springer2021-042021-04-01T00:00:00Z2022-03-28T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/31162eng2238-360310.1007/s40314-021-01484-9Castro, Luís P.Goel, NavdeepSilva, Anabela S.info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:59:13Zoai:ria.ua.pt:10773/31162Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:02:41.760463Repositório 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 A new convolution operator for the linear canonical transform with applications
title A new convolution operator for the linear canonical transform with applications
spellingShingle A new convolution operator for the linear canonical transform with applications
Castro, Luís P.
Linear canonical transform
Convolution
Integral equations
Filtering
title_short A new convolution operator for the linear canonical transform with applications
title_full A new convolution operator for the linear canonical transform with applications
title_fullStr A new convolution operator for the linear canonical transform with applications
title_full_unstemmed A new convolution operator for the linear canonical transform with applications
title_sort A new convolution operator for the linear canonical transform with applications
author Castro, Luís P.
author_facet Castro, Luís P.
Goel, Navdeep
Silva, Anabela S.
author_role author
author2 Goel, Navdeep
Silva, Anabela S.
author2_role author
author
dc.contributor.author.fl_str_mv Castro, Luís P.
Goel, Navdeep
Silva, Anabela S.
dc.subject.por.fl_str_mv Linear canonical transform
Convolution
Integral equations
Filtering
topic Linear canonical transform
Convolution
Integral equations
Filtering
description The linear canonical transform plays an important role in engineering and many applied fields, as it is the case of optics and signal processing. In this paper, a new convolution for the linear canonical transform is proposed and a corresponding product theorem is deduced. It is also proved a generalized Young's inequality for the introduced convolution operator. Moreover, necessary and sufficient conditions are obtained for the solvability of a class of convolution type integral equations associated with the linear canonical transform. Finally, the obtained results are implemented in multiplicative filters design, through the product in both the linear canonical transform domain and the time domain, where specific computations and comparisons are exposed.
publishDate 2021
dc.date.none.fl_str_mv 2021-04
2021-04-01T00:00:00Z
2022-03-28T00:00:00Z
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/10773/31162
url http://hdl.handle.net/10773/31162
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2238-3603
10.1007/s40314-021-01484-9
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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
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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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