Fractional Order Numerical Differentiation with B-Spline Functions

Da-Yan Liu (1) , Taous-Meriem Laleg-Kirati (1) , Olivier Gibaru (2, 3) , Wilfrid Perruquetti (2, 4, 5)

1 KAUST-CEMSE - Estimation Modelling and ANalysis Group
2 NON-A - Non-Asymptotic estimation for online systems
3 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
4 SyNeR - Systèmes Non Linéaires et à Retards
5 Centrale Lille

Smoothing noisy data with spline functions is well known in approximation theory. Smoothing splines have been used to deal with the problem of numerical differentiation. In this paper, we extend this method to estimate the fractional derivatives of a smooth signal from its discrete noisy data. We begin with finding a smoothing spline by solving the Tikhonov regularization problem. Then, we propose a fractional order differentiator by calculating the fractional derivative of the obtained smoothing spline. Numerical results are given to show the efficiency of the proposed method in comparison with some existing methods.

Domaines: Analyse numérique [math.NA]

Da-Yan Liu, Taous-Meriem Laleg-Kirati, Olivier Gibaru, Wilfrid Perruquetti. Fractional Order Numerical Differentiation with B-Spline Functions. The International Conference on Fractional Signals and Systems 2013, Oct 2013, Ghent, Belgium. ⟨hal-00859455⟩