Analyse fréquentielle des dérivateurs algébriques

Francisco de Asís García Collado (1) , Brigitte d'Andréa-Novel (1) , Michel Fliess (2, 3) , Hugues Mounier (4)

1 CAOR - Centre de Robotique
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 ALIEN - Algebra for Digital Identification and Estimation
4 IEF - Institut d'électronique fondamentale

This communication is devoted to the performance evaluation of new numerical differentiators, of algebraic flavor, which lead to the solution of many pending questions in control, signal and finance. The continuous-time expression of such a differentiator is an integral over a short time window of the signal multiplied by some polynomial time function. It yields a finite linear digital filter, which is easily implemented. An empirical formula is deduced, which predicts the frequency response of this filter. The computations, which are detailed for a first order derivation, are applied to experimental data in order to estimate the longitudinal acceleration of some vehicle. Our results, which are excellent, are compared to those given by a standard filter from the Matlab/Simulink toolbox.

Mots clés: Numerical differentiation; digital filters; automotive industry; operational calculus

Domaines: Traitement du signal et de l'image [eess.SP]; Automatique; Ingénierie, finance et science [cs.CE]; Finance quantitative [q-fin.CP]; Traitement du signal et de l'image [eess.SP]

Francisco de Asís García Collado, Brigitte d'Andréa-Novel, Michel Fliess, Hugues Mounier. Analyse fréquentielle des dérivateurs algébriques. XXIIe Colloque GRETSI, Sep 2009, Dijon, France. ⟨inria-00394972⟩