Title :

Fractional order differentiation by integration with Jacobi polynomials

Author(s) :

Liu, Da-Yan [Auteur]
Gibaru, Olivier [Auteur]
Laboratoire des Sciences de l'Information et des Systèmes [LSIS]
Non-Asymptotic estimation for online systems [NON-A]
Perruquetti, Wilfrid [Auteur]
Systèmes Non Linéaires et à Retards [SyNeR]
Non-Asymptotic estimation for online systems [NON-A]
Laleg-Kirati, Taous-Meriem [Auteur]

Conference title :

51st IEEE Conference on Decision and Control

City :

Hawaii

Country :

Etats-Unis d'Amérique

Start date of the conference :

2012-12-10

Publication date :

2012-12-10

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Informatique [cs]/Traitement du signal et de l'image [eess.SP]
Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL