Operator theory-based computation of linear canonical transforms

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buir.contributor.authorKoç, Aykut
buir.contributor.authorÖzaktaş, Haldun M.
dc.citation.epage9en_US
dc.citation.spage1en_US
dc.citation.volumeNumber189en_US
dc.contributor.authorKoç, Aykut
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2022-02-24T05:48:16Z
dc.date.available2022-02-24T05:48:16Z
dc.date.issued2021-08-12
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.departmentNational Magnetic Resonance Research Center (UMRAM)en_US
dc.description.abstractLinear canonical transforms (LCTs) are extensively used in many areas of science and engineering with many applications, which requires a satisfactory discrete implementation. Recently, hyperdifferential operators have been proposed as a novel way of defining the discrete LCT (DLCT). Here we first focus on improving the accuracy of this approach by considering alternative discrete coordinate multiplication and differentiation operations. We also consider canonical decompositions of LCTs and compare them with the originally proposed Iwasawa decomposition. We show that accuracy of the approximation of the continuous LCT with the DLCT can be drastically improved. The advantage and elegance of this approach lie in the fact that it reduces the problem of defining sophisticated discrete transforms to merely defining discrete coordinate multiplication and differentiation operations, by reducing the transforms to these operations. As a result of systematic investigation of possible parameters and design choices, we achieve a DLCT that is both theoretically satisfying and highly accurate.en_US
dc.embargo.release2023-08-12
dc.identifier.doi10.1016/j.sigpro.2021.108291en_US
dc.identifier.eissn1872-7557
dc.identifier.issn0165-1684
dc.identifier.urihttp://hdl.handle.net/11693/77592
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://doi.org/10.1016/j.sigpro.2021.108291en_US
dc.source.titleSignal Processingen_US
dc.subjectLinear canonical transform (LCT)en_US
dc.subjectFractional Fourier transform (FRFT)en_US
dc.subjectOperator theoryen_US
dc.subjectDiscrete transformsen_US
dc.subjectHyperdifferential operatorsen_US
dc.titleOperator theory-based computation of linear canonical transformsen_US
dc.typeArticleen_US

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Department of Electrical and Electronics Engineering
National Magnetic Resonance Research Center (UMRAM)