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A new method for estimating derivatives based on a distribution approach

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Abstract

In many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples.

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Authors and Affiliations

  1. University of Le Havre, LMAH, BP 1123, 76063, Le Havre Cedex, France

    Nathalie Verdière

  2. University of Sciences and Technologies of Lille, 59650, Villeneuve d’Ascq, France

    Lilianne Denis-Vidal

  3. University of Technology of Compiègne, BP 20 529, 60205, Compiègne, France

    Ghislaine Joly-Blanchard

Authors
  1. Nathalie Verdière
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  2. Lilianne Denis-Vidal
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  3. Ghislaine Joly-Blanchard
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Correspondence to Nathalie Verdière.

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Verdière, N., Denis-Vidal, L. & Joly-Blanchard, G. A new method for estimating derivatives based on a distribution approach. Numer Algor 61, 163–186 (2012). https://doi.org/10.1007/s11075-012-9535-4

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  • DOI: https://doi.org/10.1007/s11075-012-9535-4

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