Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product

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buir.contributor.authorHaldun M. Özaktaş
dc.citation.epage1895en_US
dc.citation.issueNumber8en_US
dc.citation.spage1885en_US
dc.citation.volumeNumber27en_US
dc.contributor.authorOktem, F. S.
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2016-02-08T09:57:37Z
dc.date.available2016-02-08T09:57:37Z
dc.date.issued2010-07-30en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractLinear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:57:37Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2010en
dc.identifier.doi10.1364/JOSAA.27.001885en_US
dc.identifier.issn1084-7529
dc.identifier.urihttp://hdl.handle.net/11693/22257
dc.language.isoEnglishen_US
dc.publisherOptical Society of Americaen_US
dc.relation.isversionofhttp://dx.doi.org/10.1364/JOSAA.27.001885en_US
dc.source.titleJournal of the Optical Society of America A: Optics and Image Science, and Visionen_US
dc.subjectEigenvalues and eigenfunctionsen_US
dc.subjectFourier transformsen_US
dc.subjectIntegral equationsen_US
dc.subjectMathematical transformationsen_US
dc.subjectMechanicsen_US
dc.subjectOptical systemsen_US
dc.subjectPhase space methodsen_US
dc.subjectFinite intervalsen_US
dc.subjectFractional Fourier domainsen_US
dc.subjectFractional orderen_US
dc.subjectIntegral transformen_US
dc.subjectLinear canonical transformen_US
dc.subjectNumber of degrees of freedomen_US
dc.subjectPhase spacesen_US
dc.subjectProcess signalsen_US
dc.subjectSpace-bandwidth producten_US
dc.subjectSpace-frequencyen_US
dc.subjectBandwidthen_US
dc.titleEquivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth producten_US
dc.typeArticleen_US

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