Fractional order differentiation by integration with Jacobi polynomials

Da-Yan Liu 1 Olivier Gibaru 2, 3 Wilfrid Perruquetti 2, 4 Taous-Meriem Laleg-Kirati 1
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess. 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.
Type de document :
Communication dans un congrès
51st IEEE Conference on Decision and Control, Dec 2012, Hawaii, United States. 2012
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Dernière modification le : mercredi 12 septembre 2018 - 01:25:57
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  • HAL Id : hal-00728406, version 1
  • ARXIV : 1209.1192

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Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti, Taous-Meriem Laleg-Kirati. Fractional order differentiation by integration with Jacobi polynomials. 51st IEEE Conference on Decision and Control, Dec 2012, Hawaii, United States. 2012. 〈hal-00728406〉

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