Signal representation and recovery under partial information, redundancy, and generalized finite extent constraints

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buir.advisorÖzaktaş, Haldun M.
dc.contributor.authorÖktem, Sevinç Figen
dc.date.accessioned2016-01-08T18:17:26Z
dc.date.available2016-01-08T18:17:26Z
dc.date.issued2009
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.descriptionAnkara : The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 2009.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2009.en_US
dc.descriptionIncludes bibliographical references leaves 143-150.en_US
dc.description.abstractWe study a number of fundamental issues and problems associated with linear canonical transforms (LCTs) and fractional Fourier transforms (FRTs). First, we study signal representation under generalized finite extent constraints. Then we turn our attention to signal recovery problems under partial and redundant information in multiple transform domains. In the signal representation part, we focus on sampling issues, the number of degrees of freedom, and the timefrequency support of the set of signals which are confined to finite intervals in two arbitrary linear canonical domains. We develop the notion of bicanonical width product, which is the generalization of the ordinary time-bandwidth product, to refer to the number of degrees of freedom of this set of signals. The bicanonical width product is shown to be the area of the time-frequency support of this set of signals, which is simply given by a parallelogram. Furthermore, these signals can be represented in these two LCT domains with the minimum number of samples given by the bicanonical width product. We prove that with these samples the discrete LCT provides a good approximation to the continuous LCT due to the underlying exact relation between them. In addition, the problem of finding the minimum number of samples to represent arbitrary signals is addressed based on the LCT sampling theorem. We show that this problem reduces to a simple geometrical problem, which aims to find the smallest parallelogram enclosing a given time-frequency support. By using this equivalence, we see that the bicanonical width product provides a better fit to the actual number of degrees of freedom of a signal as compared to the time-bandwidth product. We give theoretical bounds on the representational efficiency of this approach. In the process, we accomplish to relate LCT domains to the time-frequency plane. We show that each LCT domain is essentially a scaled FRT domain, and thus any LCT domain can be labeled by the associated fractional order, instead of its three parameters. We apply these concepts knowledge to the analysis of optical systems with arbitrary numbers of apertures. We propose a method to find the largest number of degrees of freedom that can pass through the system. Besides, we investigate the minimum number of samples to represent the wave at any plane in the system. In the signal recovery part of this thesis, we study a class of signal recovery problems where partial information in two or more fractional Fourier domains are available. We propose a novel linear algebraic approach to these problems and use the condition number as a measure of redundant information in given samples. By analyzing the effect of the number of known samples and their distributions on the condition number, we explore the redundancy and information relations between the given data under different partial information conditions.en_US
dc.description.degreeM.S.en_US
dc.description.statementofresponsibilityÖktem, Sevinç Figenen_US
dc.format.extentxiii, 150 leaves, illustrations, graphicsen_US
dc.identifier.urihttp://hdl.handle.net/11693/15358
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLinear canonical transformen_US
dc.subjectfractional Fourier transformen_US
dc.subjectbicanonical width producten_US
dc.subjectlinear canonical seriesen_US
dc.subjectlinear canonical domainen_US
dc.subjectsignal representationen_US
dc.subjectsignal recoveryen_US
dc.subjectsamplingen_US
dc.subjectfinite extenten_US
dc.subjectpartial informationen_US
dc.subjectredundancyen_US
dc.subjectcondition numberen_US
dc.subjectopticsen_US
dc.subject.lccTK5102.5 .O58 2009en_US
dc.subject.lcshSignal processing.en_US
dc.subject.lcshFourier transformations.en_US
dc.subject.lcshFractional Fourier transform.en_US
dc.titleSignal representation and recovery under partial information, redundancy, and generalized finite extent constraintsen_US
dc.typeThesisen_US

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