Fractional order differentiation by ...
Type de document :
Communication dans un congrès avec actes
Titre :
Fractional order differentiation by integration with Jacobi polynomials
Auteur(s) :
Liu, Da-Yan [Auteur]
Gibaru, Olivier [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Laboratoire des Sciences de l'Information et des Systèmes [LSIS]
Perruquetti, Wilfrid [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Systèmes Non Linéaires et à Retards [SyNeR]
Laleg-Kirati, Taous-Meriem [Auteur]
Gibaru, Olivier [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Laboratoire des Sciences de l'Information et des Systèmes [LSIS]
Perruquetti, Wilfrid [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Systèmes Non Linéaires et à Retards [SyNeR]
Laleg-Kirati, Taous-Meriem [Auteur]
Titre de la manifestation scientifique :
51st IEEE Conference on Decision and Control
Ville :
Hawaii
Pays :
Etats-Unis d'Amérique
Date de début de la manifestation scientifique :
2012-12-10
Date de publication :
2012-12-10
Discipline(s) HAL :
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]
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]
Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >
Lire la suite >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.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
Source :
Fichiers
- https://hal.inria.fr/hal-00728406/document
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- http://arxiv.org/pdf/1209.1192
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- https://hal.inria.fr/hal-00728406/document
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- https://hal.inria.fr/hal-00728406/document
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- document
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- Jacobi_fractional_order_differentiator_V1.pdf
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- 1209.1192
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