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Numerical differentiation with annihilators in noisy environment

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Abstract

Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.

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Authors and Affiliations

  1. UFR Mathématiques et Informatique, CRIP5, Université Paris Descartes, 45 rue des Saints-Pères, 75270, Paris cedex 06, France

    Mamadou Mboup

  2. CRAN (CNRS-UMR 7039), Université Henri Poincaré (Nancy I), BP 239, 54506, Vandœuvre-lès- Nancy, France

    Cédric Join

  3. Équipe MAX, LIX (CNRS-UMR 7161), École polytechnique, 91128, Palaiseau, France

    Michel Fliess

  4. EPI ALIEN INRIA, Paris, France

    Mamadou Mboup, Cédric Join & Michel Fliess

Authors
  1. Mamadou Mboup
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  2. Cédric Join
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  3. Michel Fliess
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Correspondence to Mamadou Mboup.

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Mboup, M., Join, C. & Fliess, M. Numerical differentiation with annihilators in noisy environment. Numer Algor 50, 439–467 (2009). https://doi.org/10.1007/s11075-008-9236-1

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