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dc.contributor.advisorÇetin, A. Enis
dc.contributor.authorDeprem, Zeynel
dc.date.accessioned2015-10-19T10:10:45Z
dc.date.available2015-10-19T10:10:45Z
dc.date.copyright2014-12
dc.date.issued2014-12
dc.identifier.urihttp://hdl.handle.net/11693/14015
dc.descriptionCataloged from PDF version.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, The Department of Electrical and Electronics Engineering and The Graduate School of Engineering and Science of Bilkent Univesity, 2014.en_US
dc.descriptionIncludes bibliographical references (leaves 120-131).en_US
dc.description.abstractIn this thesis sparsity and convex programming-based methods for timefrequency (TF) processing are developed. The proposed methods aim to obtain high resolution and cross-term free TF representations using sparsity and lifted projections. A crucial aspect of Time-Frequency (TF) analysis is the identification of separate components in a multi component signal. Wigner-Ville distribution is the classical tool for representing such signals but suffers from cross-terms. Other methods that are members of Cohen’s class distributions also aim to remove the cross terms by masking the Ambiguity Function (AF) but they result in reduced resolution. Most practical signals with time-varying frequency content are in the form of weighted trajectories on the TF plane and many others are sparse in nature. Therefore the problem can be cast as TF distribution reconstruction using a subset of AF domain coefficients and sparsity assumption in TF domain. Sparsity can be achieved by constraining or minimizing the l1 norm. Projections Onto Convex Sets (POCS) based l1 minimization approach is proposed to obtain a high resolution, cross-term free TF distribution. Several AF domain constraint sets are defined for TF reconstruction. Epigraph set of l1 norm, real part of AF and phase of AF are used during the iterative estimation process. A new kernel estimation method based on a single projection onto the epigraph set of l1 ball in TF domain is also proposed. The kernel based method obtains the TF representation in a faster way than the other optimization based methods. Component estimation from a multicomponent time-varying signal is considered using TF distribution and parametric maximum likelihood (ML) estimation. The initial parameters are obtained via time-frequency techniques. A method, which iterates amplitude and phase parameters separately, is proposed. The method significantly reduces the computational complexity and convergence time.en_US
dc.description.statementofresponsibilityby Zeynel Deprem.en_US
dc.format.extentxviii, 139 leaves : charts.en_US
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSparsityen_US
dc.subjectTime-frequency distributionen_US
dc.subjectCohen’s class distributionsen_US
dc.subjectPolynomial Phaseen_US
dc.subject.lccTK5102.9 .D47 2014en_US
dc.subject.lcshSignal processing.en_US
dc.subject.lcshTime-series analysis.en_US
dc.titleSparsity and convex programming in time-frequency processingen_US
dc.typeThesisen_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.publisherBilkent Universityen_US
dc.description.degreePh.D.en_US
dc.identifier.itemidB149365


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