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dc.contributor.authorLiu, Da-Yan
dc.contributor.authorTian, Yang
dc.contributor.authorBoutat, Driss
dc.contributor.authorLaleg-Kirati, Taous-Meriem
dc.date.accessioned2015-05-03T13:35:57Z
dc.date.available2015-05-03T13:35:57Z
dc.date.issued2015-05-02
dc.identifier.citationAn algebraic fractional order differentiator for a class of signals satisfying a linear differential equation 2015 Signal Processing
dc.identifier.issn01651684
dc.identifier.doi10.1016/j.sigpro.2015.04.017
dc.identifier.urihttp://hdl.handle.net/10754/552120
dc.description.abstractThis paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.
dc.publisherElsevier BV
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0165168415001528
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Signal Processing. 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 Signal Processing, 30 April 2015. DOI: 10.1016/j.sigpro.2015.04.017
dc.subjectFractional order differentiator
dc.subjectRiemann-Liouville derivative
dc.subjectAlgebraic parametric method
dc.subjectModulating functions method
dc.subjectUnknown input
dc.subjectNoise error analysis
dc.titleAn algebraic fractional order differentiator for a class of signals satisfying a linear differential equation
dc.typeArticle
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.departmentEstimation, Modeling and ANalysis Group
dc.identifier.journalSignal Processing
dc.eprint.versionPost-print
dc.contributor.institutionINSA Centre Val de Loire, Université d'Orléans, PRISME EA 4229, Bourges Cedex 18022, France
dc.contributor.institutionSino-French Joint Laboratory of Automation and Signal Processing, School of Automation, Nanjing University of Science and Technology, Nanjing, China
kaust.personLaleg-Kirati, Taous-Meriem
refterms.dateFOA2017-04-30T00:00:00Z
dc.date.published-online2015-05-02
dc.date.published-print2015-11


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