Fractional order differentiation by integration with Jacobi polynomials

Handle URI:
http://hdl.handle.net/10754/565864
Title:
Fractional order differentiation by integration with Jacobi polynomials
Authors:
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 )
Abstract:
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
Conference/Event name:
51st IEEE Conference on Decision and Control, CDC 2012
Issue Date:
Dec-2012
DOI:
10.1109/CDC.2012.6426436
ARXIV:
arXiv:1209.1192v1
Type:
Conference Paper
ISSN:
01912216
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLiu, Dayanen
dc.contributor.authorGibaru, O.en
dc.contributor.authorPerruquetti, Wilfriden
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.date.accessioned2015-08-11T13:44:03Zen
dc.date.available2015-08-11T13:44:03Zen
dc.date.issued2012-12en
dc.identifier.issn01912216en
dc.identifier.doi10.1109/CDC.2012.6426436en
dc.identifier.urihttp://hdl.handle.net/10754/565864en
dc.description.abstractThe differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.titleFractional order differentiation by integration with Jacobi polynomialsen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journal2012 IEEE 51st IEEE Conference on Decision and Control (CDC)en
dc.conference.date10 December 2012 through 13 December 2012en
dc.conference.name51st IEEE Conference on Decision and Control, CDC 2012en
dc.conference.locationMaui, HIen
dc.identifier.arxividarXiv:1209.1192v1en
kaust.authorLiu, Dayanen
kaust.authorLaleg-Kirati, Taous-Meriemen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.