Discrete linear canonical transform based on hyperdifferential operators

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buir.contributor.authorKoç, Aykut
buir.contributor.authorBartan, Burak
buir.contributor.authorÖzaktaş, Haldun
dc.citation.epage2248en_US
dc.citation.issueNumber9en_US
dc.citation.spage2237en_US
dc.citation.volumeNumber67en_US
dc.contributor.authorKoç, Aykuten_US
dc.contributor.authorBartan, Buraken_US
dc.contributor.authorÖzaktaş, Haldunen_US
dc.date.accessioned2020-02-05T06:34:36Z
dc.date.available2020-02-05T06:34:36Z
dc.date.issued2019-05
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.departmentNational Magnetic Resonance Research Center (UMRAM)en_US
dc.description.abstractLinear canonical transforms (LCTs) are of importance in many areas of science and engineering with many applications. Therefore, a satisfactory discrete implementation is of considerable interest. Although there are methods that link the samples of the input signal to the samples of the linear canonical transformed output signal, no widely-accepted definition of the discrete LCT has been established. We introduce a new approach to defining the discrete linear canonical transform (DLCT) by employing operator theory. Operators are abstract entities that can have both continuous and discrete concrete manifestations. Generating the continuous and discrete manifestations of LCTs from the same abstract operator framework allows us to define the continuous and discrete transforms in a structurally analogous manner. By utilizing hyperdifferential operators, we obtain a DLCT matrix, which is totally compatible with the theory of the discrete Fourier transform (DFT) and its dual and circulant structure, which makes further analytical manipulations and progress possible. The proposed DLCT is to the continuous LCT, what the DFT is to the continuous Fourier transform. The DLCT of the signal is obtained simply by multiplying the vector holding the samples of the input signal by the DLCT matrix.en_US
dc.identifier.doi10.1109/TSP.2019.2903031en_US
dc.identifier.eissn1941-0476
dc.identifier.issn1053-587X
dc.identifier.urihttp://hdl.handle.net/11693/53072
dc.language.isoEnglishen_US
dc.publisherIEEEen_US
dc.relation.isversionofhttps://doi.org/10.1109/TSP.2019.2903031en_US
dc.source.titleIEEE Transactions on Signal Processingen_US
dc.subjectLinear canonical transform (LCT)en_US
dc.subjectFractional Fourier transform (FRT)en_US
dc.subjectOperator theoryen_US
dc.subjectDiscrete transformsen_US
dc.subjectHyperdifferential operatorsen_US
dc.titleDiscrete linear canonical transform based on hyperdifferential operatorsen_US
dc.typeArticleen_US
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Department of Electrical and Electronics Engineering
National Magnetic Resonance Research Center (UMRAM)