Relaxed quaternionic Gabor expansions at critical density

Detalhes bibliográficos
Autor(a) principal: Hartmann, Stefan
Data de Publicação: 2015
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/14592
Resumo: Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique l2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion.
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spelling Relaxed quaternionic Gabor expansions at critical densityGabor expansionCritical densityShifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique l2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion.Wiley2015-09-01T16:09:20Z2015-06-17T00:00:00Z2015-06-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/14592eng1099-1476Hartmann, Stefaninfo: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:RCAAP2024-02-22T11:26:20Zoai:ria.ua.pt:10773/14592Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:00.991541Repositório 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 Relaxed quaternionic Gabor expansions at critical density
title Relaxed quaternionic Gabor expansions at critical density
spellingShingle Relaxed quaternionic Gabor expansions at critical density
Hartmann, Stefan
Gabor expansion
Critical density
title_short Relaxed quaternionic Gabor expansions at critical density
title_full Relaxed quaternionic Gabor expansions at critical density
title_fullStr Relaxed quaternionic Gabor expansions at critical density
title_full_unstemmed Relaxed quaternionic Gabor expansions at critical density
title_sort Relaxed quaternionic Gabor expansions at critical density
author Hartmann, Stefan
author_facet Hartmann, Stefan
author_role author
dc.contributor.author.fl_str_mv Hartmann, Stefan
dc.subject.por.fl_str_mv Gabor expansion
Critical density
topic Gabor expansion
Critical density
description Shifted and modulated Gaussian functions play a vital role in the representation of signals. We extend the theory into a quaternionic setting, using two exponential kernels with two complex numbers. As a final result, we show that every continuous and quaternion-valued signal f in the Wiener space can be expanded into a unique l2 series on a lattice at critical density 1, provided one more point is added in the middle of a cell. We call that a relaxed Gabor expansion.
publishDate 2015
dc.date.none.fl_str_mv 2015-09-01T16:09:20Z
2015-06-17T00:00:00Z
2015-06-17
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/10773/14592
url http://hdl.handle.net/10773/14592
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1099-1476
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Wiley
publisher.none.fl_str_mv Wiley
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
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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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