Optimal compactness of fractional Fourier domain characterizes frequency modulated signals

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dc.contributor.affiliationUgarte, J.P., GIMSC, Universidad de San Buenaventura, Medellin, Colombia
dc.contributor.affiliationGómez-Echavarría, A., MATBIOM, Universidad de Medellin, Medellin, Colombia
dc.contributor.affiliationTobón, C., MATBIOM, Universidad de Medellin, Medellin, Colombia
dc.contributor.authorUgarte J.P
dc.contributor.authorGómez-Echavarría A
dc.contributor.authorTobón C.
dc.date.accessioned2024-07-31T21:07:20Z
dc.date.available2024-07-31T21:07:20Z
dc.date.issued2023
dc.descriptionThe Fourier transform (FT) is a mathematical tool widely used in signal processing applications; however, it presents limitations when dealing with non-stationary time series. By considering the fractional powers of the FT operator, a generalized version is obtained known as the fractional FT. This transformation allows free rotations of the time–frequency plane that can be exploited for processing frequency modulated signals. This work addresses the problem of characterizing noisy, multicomponent, and non-linear frequency modulated signals through a proper order of the fractional FT, whose kernel consists of a chirp with linear frequency modulation. The estimation of the optimal fractional FT order obeys a strategy that includes the quantification of the compactness of fractional Fourier domains and the search for the order that leads to the most compact domain. For this purpose, five compactness measures are assessed in combination with four different optimization algorithms. Numerical experiments are performed on synthetic signals, generated under distinct frequency modulation conditions, and on real acoustic signals. The results reveal that the spectral second moment and the spectral entropy provide robust and reliable measures of the compactness of the fractional Fourier domain. These metrics enable an effective computation of the optimal fractional order that describes the frequency modulation content of the underlying signal. The optimization algorithms assessed in this study yield similar estimations of the optimal fractional order, yet the coarse-to-fine algorithm is more efficient in terms of computation time, followed by the particle swarm optimization algorithm. Moreover, it is verified that the strategy can be adopted for extracting dynamical information of the frequency modulation content from synthetic signals with multiple linear and non-linear components and from real acoustic data, e.g., bat and bird recordings. The extensive assessment of the signal processing strategy based on the fractional FT outlined in this work provides relevant information for exploring further applications with time series captured when studying complex and non-stationary processes, such as biological, medical, or economic systems. © 2023 Elsevier Ltd
dc.identifier.doi10.1016/j.chaos.2023.114291
dc.identifier.instnameinstname:Universidad de Medellínspa
dc.identifier.issn9600779
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.repourlrepourl:https://repository.udem.edu.co/
dc.identifier.urihttp://hdl.handle.net/11407/8547
dc.language.isoeng
dc.publisherElsevier Ltdspa
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.relation.citationvolume177
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85177732413&doi=10.1016%2fj.chaos.2023.114291&partnerID=40&md5=6388490c47890a6e3bf730ea8f57e307
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dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.sourceChaos, Solitons and Fractals
dc.sourceChaos Solitons Fractals
dc.sourceScopus
dc.subjectBioacoustic signalseng
dc.subjectDynamical analysiseng
dc.subjectMetaheuristicseng
dc.subjectNon-stationary signalseng
dc.subjectChirp modulationeng
dc.subjectComputational efficiencyeng
dc.subjectFourier serieseng
dc.subjectFrequency estimationeng
dc.subjectParticle swarm optimization (PSO)eng
dc.subjectTime serieseng
dc.subjectBioacoustic signalseng
dc.subjectDynamical analysiseng
dc.subjectFractional Fourier domainseng
dc.subjectFractional Fourier transformseng
dc.subjectFractional ordereng
dc.subjectFrequency modulated signaleng
dc.subjectMetaheuristiceng
dc.subjectNonstationary signalseng
dc.subjectOptimization algorithmseng
dc.subjectSynthetic signalseng
dc.subjectFrequency modulationeng
dc.titleOptimal compactness of fractional Fourier domain characterizes frequency modulated signalseng
dc.typearticle
dc.type.localArtículospa
dc.type.versioninfo:eu-repo/semantics/publishedVersion

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