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dc.contributor.authorLevie, Ron
dc.contributor.authorAvron, Haim
dc.contributor.authorKutyniok, Gitta Astrid Hildegard
dc.date.accessioned2024-03-22T08:00:40Z
dc.date.available2024-03-22T08:00:40Z
dc.date.issued2022-09-30
dc.description.abstractWe study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such methods using a quasi-Monte Carlo (QMC) approach. We consider cases where the time-frequency representation is redundant, having feature axes in addition to the time and frequency axes. The proposed QMC method allows sampling both efficiently and evenly such redundant time-frequency representations. Indeed, 1) the number of samples required for a certain accuracy is log-linear in the resolution of the signal space, and depends only weakly on the dimension of the redundant time-frequency space, and 2) the quasi-random samples have low discrepancy, so they are spread evenly in the redundant time-frequency space. One example of such redundant representation is the localizing time-frequency transform (LTFT), where the time-frequency plane is enhanced by a third axis. This higher dimensional time-frequency space improves the quality of some time-frequency signal processing tasks, like the phase vocoder (an audio signal processing effect). Since the computational complexity of the QMC is log-linear in the resolution of the signal space, this higher dimensional time-frequency space does not degrade the computation complexity of the proposed QMC method. The proposed QMC method is more efficient than standard Monte Carlo methods, since the deterministic QMC sample points are optimally spread in the time-frequency space, while random samples are not.en_US
dc.identifier.citationLevie, Avron, Kutyniok. Quasi Monte Carlo time-frequency analysis. Journal of Mathematical Analysis and Applications. 2023;518(2):1-37en_US
dc.identifier.cristinIDFRIDAID 2131505
dc.identifier.doi10.1016/j.jmaa.2022.126732
dc.identifier.issn0022-247X
dc.identifier.issn1096-0813
dc.identifier.urihttps://hdl.handle.net/10037/33225
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.relation.journalJournal of Mathematical Analysis and Applications
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2023 The Author(s)en_US
dc.titleQuasi Monte Carlo time-frequency analysisen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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