Robust fractional order differentiators using generalized modulating functions method

dc.contributor.authorLiu, Dayan
dc.contributor.authorLaleg-Kirati, Taous-Meriem
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputational Bioscience Research Center (CBRC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentElectrical Engineering Program
dc.contributor.institutionINSA Centre Val de Loire, Université DOrléans, PRISME EA 4229Bourges, France
dc.date.accessioned2015-08-03T12:29:19Z
dc.date.available2015-08-03T12:29:19Z
dc.date.issued2015-02
dc.description.abstractThis paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
dc.eprint.versionPre-print
dc.identifier.citationLiu, D.-Y., & Laleg-Kirati, T.-M. (2015). Robust fractional order differentiators using generalized modulating functions method. Signal Processing, 107, 395–406. doi:10.1016/j.sigpro.2014.05.016
dc.identifier.doi10.1016/j.sigpro.2014.05.016
dc.identifier.issn0165-1684
dc.identifier.journalSignal Processing
dc.identifier.urihttp://hdl.handle.net/10754/564036
dc.publisherElsevier BV
dc.relation.urlhttps://hal.inria.fr/hal-00923748v3/file/Exact_fractional_differentiator.pdf
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [JournalTitle], [[Volume], [Issue], (2015-02)] DOI: 10.1016/j.sigpro.2014.05.016 . © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsThis file is an open access version redistributed from: https://hal.inria.fr/hal-00923748v3/file/Exact_fractional_differentiator.pdf
dc.subjectFractional order differentiator
dc.subjectGeneralized modulating functions method
dc.subjectNoise
dc.subjectRiemann-Liouville derivative
dc.titleRobust fractional order differentiators using generalized modulating functions method
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Liu, Dayan,equals">Liu, Dayan</a><br><a href="https://repository.kaust.edu.sa/search?query=orcid.id:0000-0001-5944-0121&spc.sf=dc.date.issued&spc.sd=DESC">Laleg-Kirati, Taous-Meriem</a> <a href="https://orcid.org/0000-0001-5944-0121" target="_blank"><img src="https://repository.kaust.edu.sa/server/api/core/bitstreams/82a625b4-ed4b-40c8-865a-d6a5225a26a4/content" width="16" height="16"/></a><br><br><h5>KAUST Department</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Applied Mathematics and Computational Science Program,equals">Applied Mathematics and Computational Science Program</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computational Bioscience Research Center (CBRC),equals">Computational Bioscience Research Center (CBRC)</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division,equals">Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.department=Electrical Engineering Program,equals">Electrical Engineering Program</a><br><br><h5>Date</h5>2015-02</span>
display.details.right<span><h5>Abstract</h5>This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.<br><br><h5>Citation</h5>Liu, D.-Y., & Laleg-Kirati, T.-M. (2015). Robust fractional order differentiators using generalized modulating functions method. Signal Processing, 107, 395–406. doi:10.1016/j.sigpro.2014.05.016<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Elsevier BV,equals">Elsevier BV</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Signal Processing,equals">Signal Processing</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1016/j.sigpro.2014.05.016">10.1016/j.sigpro.2014.05.016</a><br><br><h5>Additional Links</h5>https://hal.inria.fr/hal-00923748v3/file/Exact_fractional_differentiator.pdf</span>
kaust.personLaleg-Kirati, Taous-Meriem
kaust.personLiu, Dayan
orcid.authorLiu, Dayan
orcid.authorLaleg-Kirati, Taous-Meriem::0000-0001-5944-0121
orcid.id0000-0001-5944-0121
refterms.dateFOA2023-09-18T13:56:06Z
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