An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

Handle URI:
http://hdl.handle.net/10754/552120
Title:
An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation
Authors:
Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Abstract:
This 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation 2015 Signal Processing
Publisher:
Elsevier BV
Journal:
Signal Processing
Issue Date:
30-Apr-2015
DOI:
10.1016/j.sigpro.2015.04.017
Type:
Article
ISSN:
01651684
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0165168415001528
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Da-Yanen
dc.contributor.authorTian, Yangen
dc.contributor.authorBoutat, Drissen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.date.accessioned2015-05-03T13:35:57Zen
dc.date.available2015-05-03T13:35:57Zen
dc.date.issued2015-04-30en
dc.identifier.citationAn algebraic fractional order differentiator for a class of signals satisfying a linear differential equation 2015 Signal Processingen
dc.identifier.issn01651684en
dc.identifier.doi10.1016/j.sigpro.2015.04.017en
dc.identifier.urihttp://hdl.handle.net/10754/552120en
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.en
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0165168415001528en
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.2015.04.017en
dc.subjectFractional order differentiatoren
dc.subjectRiemann-Liouville derivativeen
dc.subjectAlgebraic parametric methoden
dc.subjectModulating functions methoden
dc.subjectUnknown inputen
dc.subjectNoise error analysisen
dc.titleAn algebraic fractional order differentiator for a class of signals satisfying a linear differential equationen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSignal Processingen
dc.eprint.versionPost-printen
dc.contributor.institutionINSA Centre Val de Loire, Université d'Orléans, PRISME EA 4229, Bourges Cedex 18022, Franceen
dc.contributor.institutionSino-French Joint Laboratory of Automation and Signal Processing, School of Automation, Nanjing University of Science and Technology, Nanjing, Chinaen
kaust.authorLaleg-Kirati, Taous-Meriemen
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