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Hyperbolic linear canonical transforms of quaternion signals and uncertainty

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dc.contributor.authorMorais, J.
dc.contributor.authorFerreira, M.
dc.date.accessioned2023-04-10T16:44:26Z
dc.date.embargo2025-08
dc.date.issued2023
dc.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.2023.127971pt_PT
dc.descriptionAcknowledgements: 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.
dc.description.abstractThis 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationJ. Morais and M. Ferreira, Hyperbolic linear canonical transforms of quaternion signals and uncertainty, Applied Mathematics and Computation (450), 2023, Article 127971.pt_PT
dc.identifier.doihttps://doi.org/10.1016/j.amc.2023.127971pt_PT
dc.identifier.eissn1873-5649
dc.identifier.issn0096-3003
dc.identifier.other127971
dc.identifier.urihttp://hdl.handle.net/10400.8/8357
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relationCenter for Research and Development in Mathematics and Applications
dc.relationNot Available
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0096300323001406pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/pt_PT
dc.subjectQuaternionic Analysispt_PT
dc.subjectQuaternion Hyperbolic Linear Canonical Transformspt_PT
dc.subjectPlancherel and Parseval Theoremspt_PT
dc.subjectRiemann-Lebesgue Lemmapt_PT
dc.subjectHeisenberg uncertainty principlespt_PT
dc.titleHyperbolic linear canonical transforms of quaternion signals and uncertaintypt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardTitleCenter for Research and Development in Mathematics and Applications
oaire.awardTitleNot Available
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04106%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/CEEC IND 2018/CEECIND%2F01131%2F2018%2FCP1559%2FCT0014/PT
oaire.citation.titleApplied Mathematics and Computationpt_PT
oaire.citation.volume450pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStreamCEEC IND 2018
person.familyNameMorais
person.familyNameFerreira
person.givenNameJoao
person.givenNameMilton
person.identifier.ciencia-idCA19-2009-F26D
person.identifier.orcid0000-0001-7045-0224
person.identifier.orcid0000-0003-1816-8293
person.identifier.ridA-2004-2015
person.identifier.scopus-author-id19639247200
person.identifier.scopus-author-id12144179800
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsembargoedAccesspt_PT
rcaap.typearticlept_PT
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relation.isAuthorOfPublication.latestForDiscovery085b25f7-c6a5-449e-9729-ddafe6b56876
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