Linear canonical domains and degrees of freedom of signals and systems

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dc.citation.epage239en_US
dc.citation.spage197en_US
dc.citation.volumeNumber198en_US
dc.contributor.authorÖktem, F. S.en_US
dc.contributor.authorÖzaktaş, Haldunen_US
dc.contributor.editorHealy, J. J.
dc.contributor.editorKutay, Mehmet Alper
dc.contributor.editorÖzaktaş, Haldun
dc.contributor.editorSheridan, J. T.
dc.date.accessioned2018-04-12T13:53:53Z
dc.date.available2018-04-12T13:53:53Z
dc.date.issued2016en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.descriptionChapter 7
dc.description.abstractWe discuss the relationships between linear canonical transform (LCT) domains, fractional Fourier transform (FRT) domains, and the space-frequency plane. In particular, 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 monotonically ordered by the corresponding fractional order parameter and provides a more transparent view of the evolution of light through an optical system modeled by LCTs. We then study the number of degrees of freedom of optical systems and signals based on these concepts. We first discuss the bicanonical width product (BWP), which is the number of degrees of freedom of LCT-limited signals. The BWP generalizes the space-bandwidth product and often provides a tighter measure of the actual number of degrees of freedom of signals. We illustrate the usefulness of the notion of BWP in two applications: efficient signal representation and efficient system simulation. In the first application we provide a sub-Nyquist sampling approach to represent and reconstruct signals with arbitrary space-frequency support. In the second application we provide a fast discrete LCT (DLCT) computation method which can accurately compute a (continuous) LCT with the minimum number of samples given by the BWP. Finally, we focus on the degrees of freedom of first-order optical systems with multiple apertures. We show how to explicitly quantify the degrees of freedom of such systems, state conditions for lossless transfer through the system and analyze the effects of lossy transfer.en_US
dc.identifier.doi10.1007/978-1-4939-3028-9_7en_US
dc.identifier.doihttps://doi.org/10.1007/978-1-4939-3028-9
dc.identifier.eisbn9781493930289
dc.identifier.isbn9781493930272
dc.identifier.urihttp://hdl.handle.net/11693/38354
dc.language.isoEnglishen_US
dc.publisherSpringer Verlagen_US
dc.relation.ispartofLinear canonical transforms
dc.relation.ispartofseriesSpringer series in optical sciences
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-1-4939-3028-9_7en_US
dc.subjectSampling theoremen_US
dc.subjectWigner distributionen_US
dc.subjectSystem windowen_US
dc.subjectIwasawa decompositionen_US
dc.subjectLinear canonical transformen_US
dc.titleLinear canonical domains and degrees of freedom of signals and systemsen_US
dc.typeBook Chapteren_US
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