Linearly time-varying systems and their fast implementation

buir.contributor.authorÖzaktaş, Haldun M.
dc.citation.epage10en_US
dc.citation.spage1
dc.citation.volumeNumber142
dc.contributor.authorCandogan, U.
dc.contributor.authorCandogan, O.
dc.contributor.authorÖzaktaş, Haldun M.
dc.date.accessioned2024-03-14T07:29:51Z
dc.date.available2024-03-14T07:29:51Z
dc.date.issued2023-08-22
dc.departmentDepartment of Electrical and Electronics Engineering
dc.description.abstractLinear time-invariant systems can be implemented in O(N log N) time, whereas the most general family of linear systems can be implemented as a vector-matrix product in O(N2) time. However, there are time-variant systems that can be implemented in O(N log N) time. In this paper, we introduce a particular family of such systems, which we refer to as the class of linearly time varying (LTV) systems. These systems interpolate between multiplicative systems and convolutive systems, and are characterized by their chirp-type eigenfunctions and their relationship to fractional Fourier domain filtering. We derive expressions for the linear transform kernel of LTV systems, and illustrate their use with examples. Recognizing LTV systems, or approximating linear systems with LTV systems when possible, can reduce the time of computation from O(N2) to O(N log N).
dc.embargo.release2025-08-22
dc.identifier.doi10.1016/j.dsp.2023.104200
dc.identifier.eissn1095-4333
dc.identifier.issn1051-2004
dc.identifier.urihttps://hdl.handle.net/11693/114719
dc.language.isoen
dc.publisherElsevier
dc.relation.isversionofhttps://doi.org/10.1016/j.dsp.2023.104200
dc.rightsCC BY-NC-ND (Attribution-NonCommercial-NoDerivs 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source.titleDigital Signal Processing
dc.subjectFast algorithms for digital signal processing
dc.subjectAlgorithms for signal filtering, restoration, enhancement, and reconstruction
dc.subjectTransforms for signal processing
dc.titleLinearly time-varying systems and their fast implementation
dc.typeArticle

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