Fractional order differentiation by integration with Jacobi polynomials

Dayan Liu, O. Gibaru, Wilfrid Perruquetti, Taous-Meriem Laleg-Kirati

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Scopus citations


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.
Original languageEnglish (US)
Title of host publication2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages6
ISBN (Print)9781467320665
StatePublished - Dec 2012


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