The Fractional Fourier transform and harmonic oscillation

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buir.contributor.authorHaldun M. Özaktaş
dc.citation.epage172en_US
dc.citation.issueNumber1-4en_US
dc.citation.spage157en_US
dc.citation.volumeNumber29en_US
dc.contributor.authorKutay, M. A.
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2018-04-12T13:46:08Z
dc.date.available2018-04-12T13:46:08Z
dc.date.issued2002en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractThe ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order fractional Fourier transform is equal to the ordinary Fourier transform. This paper discusses the relationship of the fractional Fourier transform to harmonic oscillation; both correspond to rotation in phase space. Various important properties of the transform are discussed along with examples of common transforms. Some of the applications of the transform are briefly reviewed.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T13:46:08Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2002en
dc.identifier.doi10.1023/A:1016543123400en_US
dc.identifier.issn0924-090X
dc.identifier.urihttp://hdl.handle.net/11693/38159
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1023/A:1016543123400en_US
dc.source.titleNonlinear Dynamicsen_US
dc.subjectFractional Fourier transformen_US
dc.subjectGreen's functionen_US
dc.subjectHarmonic oscillationen_US
dc.subjectPhase spaceen_US
dc.subjectEigenvalues and eigenfunctionsen_US
dc.subjectHarmonic analysisen_US
dc.subjectMathematical operatorsen_US
dc.subjectOscillationsen_US
dc.subjectPerturbation techniquesen_US
dc.subjectPhase space methodsen_US
dc.subjectWave equationsen_US
dc.subjectHarmonic oscillationsen_US
dc.subjectFourier transformsen_US
dc.titleThe Fractional Fourier transform and harmonic oscillationen_US
dc.typeArticleen_US

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