Time-frequency analysis of signals using support adaptive Hermite-Gaussian expansions

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buir.contributor.authorArıkan, Orhan
buir.contributor.orcidArıkan, Orhan|0000-0002-3698-8888
dc.citation.epage1023en_US
dc.citation.issueNumber6en_US
dc.citation.spage1010en_US
dc.citation.volumeNumber22en_US
dc.contributor.authorAlp, Y. K.en_US
dc.contributor.authorArıkan, Orhanen_US
dc.date.accessioned2016-02-08T09:43:12Z
dc.date.available2016-02-08T09:43:12Z
dc.date.issued2012-05-18en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractSince Hermite-Gaussian (HG) functions provide an orthonormal basis with the most compact time-frequency supports (TFSs), they are ideally suited for time-frequency component analysis of finite energy signals. For a signal component whose TFS tightly fits into a circular region around the origin, HG function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components whose TFS has a non-circular shape away from the origin, straight forward expansions require excessively large number of HGs resulting to noise fitting. Furthermore, for closely spaced signal components with non-circular TFSs, direct application of HG expansion cannot provide reliable estimates to the individual signal components. To alleviate these problems, by using expectation maximization (EM) iterations, we propose a fully automated pre-processing technique which identifies and transforms TFSs of individual signal components to circular regions centered around the origin so that reliable signal estimates for the signal components can be obtained. The HG expansion order for each signal component is determined by using a robust estimation technique. Then, the estimated components are post-processed to transform their TFSs back to their original positions. The proposed technique can be used to analyze signals with overlapping components as long as the overlapped supports of the components have an area smaller than the effective support of a Gaussian atom which has the smallest time-bandwidth product. It is shown that if the area of the overlap region is larger than this threshold, the components cannot be uniquely identified. Obtained results on the synthetic and real signals demonstrate the effectiveness for the proposed time-frequency analysis technique under severe noise cases.en_US
dc.identifier.doi10.1016/j.dsp.2012.05.005en_US
dc.identifier.issn1051-2004
dc.identifier.urihttp://hdl.handle.net/11693/21216
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.dsp.2012.05.005en_US
dc.source.titleDigital Signal Processing: A Review Journalen_US
dc.subjectHermite-Gaussian functionen_US
dc.subjectOrthonormal basisen_US
dc.subjectSignal componenten_US
dc.subjectTime-frequency supporten_US
dc.subjectBasis functionsen_US
dc.subjectCircular regionen_US
dc.subjectComponent analysisen_US
dc.subjectExpectation maximizationen_US
dc.subjectFinite energyen_US
dc.subjectFunction expansionen_US
dc.subjectGaussiansen_US
dc.subjectHermite-Gaussian functionen_US
dc.subjectNon-circularen_US
dc.subjectOrthonormal basisen_US
dc.subjectOverlap regionen_US
dc.subjectOverlapping componentsen_US
dc.subjectPre-processingen_US
dc.subjectReal signalsen_US
dc.subjectReliable estimatesen_US
dc.subjectRobust estimationen_US
dc.subjectSignal componentsen_US
dc.subjectTime frequencyen_US
dc.subjectTime frequency analysisen_US
dc.subjectTime-bandwidth productsen_US
dc.subjectEstimationen_US
dc.subjectGaussian distributionen_US
dc.subjectMercury compoundsen_US
dc.subjectExpansionen_US
dc.titleTime-frequency analysis of signals using support adaptive Hermite-Gaussian expansionsen_US
dc.typeArticleen_US

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