Hyperbolic linear canonical transforms of quaternion signals and uncertainty
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2023 |
| 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/10400.8/8357 |
Resumo: | *The final version is published in Applied Mathematics and Computation (450), 2023, Article 127971. It as available via the website https://doi.org/10.1016/j.amc.2023.127971 |
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Hyperbolic linear canonical transforms of quaternion signals and uncertaintyQuaternionic AnalysisQuaternion Hyperbolic Linear Canonical TransformsPlancherel and Parseval TheoremsRiemann-Lebesgue LemmaHeisenberg uncertainty principles*The final version is published in Applied Mathematics and Computation (450), 2023, Article 127971. It as available via the website https://doi.org/10.1016/j.amc.2023.127971Acknowledgements: The first author’s work was supported by the Asociaci´on Mexicana de Cultura, A. C.. The work of M. Ferreira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT – Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/202.This paper is concerned with Linear Canonical Transforms (LCTs) associated with two-dimensional quaternion-valued signals defined in an open rectangle of the Euclidean plane endowed with a hyperbolic measure, which we call Quaternion Hyperbolic Linear Canonical Transforms (QHLCTs). These transforms are defined by replacing the Euclidean plane wave with a corresponding hyperbolic relativistic plane wave in one dimension multiplied by quadratic modulations in both the hyperbolic spatial and frequency domains, giving the hyperbolic counterpart of the Euclidean LCTs. We prove the fundamental properties of the partial QHLCTs and the right-sided QHLCT by employing hyperbolic geometry tools and establish main results such as the Riemann-Lebesgue Lemma, the Plancherel and Parseval Theorems, and inversion formulas. The analysis is carried out in terms of novel hyperbolic derivative and hyperbolic primitive concepts, which lead to the differentiation and integration properties of the QHLCTs. The results are applied to establish two quaternionic versions of the Heisenberg uncertainty principle for the right-sided QHLCT. These uncertainty principles prescribe a lower bound on the product of the effective widths of quaternion-valued signals in the hyperbolic spatial and frequency domains. It is shown that only hyperbolic Gaussian quaternion functions minimize the uncertainty relations.ElsevierIC-OnlineMorais, J.Ferreira, M.20232025-08-01T00:00:00Z2023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/10400.8/8357engJ. Morais and M. Ferreira, Hyperbolic linear canonical transforms of quaternion signals and uncertainty, Applied Mathematics and Computation (450), 2023, Article 127971.0096-3003127971https://doi.org/10.1016/j.amc.2023.1279711873-5649info: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:RCAAP2024-01-17T15:57:09Zoai:iconline.ipleiria.pt:10400.8/8357Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:51:05.755730Repositório 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 |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| title |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| spellingShingle |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty Morais, J. Quaternionic Analysis Quaternion Hyperbolic Linear Canonical Transforms Plancherel and Parseval Theorems Riemann-Lebesgue Lemma Heisenberg uncertainty principles |
| title_short |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| title_full |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| title_fullStr |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| title_full_unstemmed |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| title_sort |
Hyperbolic linear canonical transforms of quaternion signals and uncertainty |
| author |
Morais, J. |
| author_facet |
Morais, J. Ferreira, M. |
| author_role |
author |
| author2 |
Ferreira, M. |
| author2_role |
author |
| dc.contributor.none.fl_str_mv |
IC-Online |
| dc.contributor.author.fl_str_mv |
Morais, J. Ferreira, M. |
| dc.subject.por.fl_str_mv |
Quaternionic Analysis Quaternion Hyperbolic Linear Canonical Transforms Plancherel and Parseval Theorems Riemann-Lebesgue Lemma Heisenberg uncertainty principles |
| topic |
Quaternionic Analysis Quaternion Hyperbolic Linear Canonical Transforms Plancherel and Parseval Theorems Riemann-Lebesgue Lemma Heisenberg uncertainty principles |
| description |
*The final version is published in Applied Mathematics and Computation (450), 2023, Article 127971. It as available via the website https://doi.org/10.1016/j.amc.2023.127971 |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023 2023-01-01T00:00:00Z 2025-08-01T00:00:00Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/article |
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article |
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publishedVersion |
| dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.8/8357 |
| url |
http://hdl.handle.net/10400.8/8357 |
| dc.language.iso.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
J. Morais and M. Ferreira, Hyperbolic linear canonical transforms of quaternion signals and uncertainty, Applied Mathematics and Computation (450), 2023, Article 127971. 0096-3003 127971 https://doi.org/10.1016/j.amc.2023.127971 1873-5649 |
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info:eu-repo/semantics/embargoedAccess |
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application/pdf application/pdf |
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Elsevier |
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Elsevier |
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