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Analyse fréquentielle des dérivateurs algébriques

Author

Listed:
  • Francisco de Asís García Collado

    (CAOR - Centre de Robotique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres)

  • Brigitte d'Andréa-Novel

    (CAOR - Centre de Robotique - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris Sciences et Lettres)

  • Michel Fliess

    (LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, ALIEN - Algebra for Digital Identification and Estimation - Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - Centrale Lille - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Hugues Mounier

    (IEF - Institut d'électronique fondamentale - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Francisco de Asís García Collado & Brigitte d'Andréa-Novel & Michel Fliess & Hugues Mounier, 2009. "Analyse fréquentielle des dérivateurs algébriques," Post-Print inria-00394972, HAL.
    • Handle: RePEc:hal:journl:inria-00394972
    Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00394972
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