Numerical Algorithms

, Volume 61, Issue 1, pp 163–186 | Cite as

A new method for estimating derivatives based on a distribution approach

  • Nathalie Verdière
  • Lilianne Denis-Vidal
  • Ghislaine Joly-Blanchard
Original Paper

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.

Keywords

Derivatives estimation Distributions Test Functions 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Nathalie Verdière
    • 1
  • Lilianne Denis-Vidal
    • 2
  • Ghislaine Joly-Blanchard
    • 3
  1. 1.University of Le Havre, LMAHLe Havre CedexFrance
  2. 2.University of Sciences and Technologies of LilleVilleneuve d’AscqFrance
  3. 3.University of Technology of CompiègneCompiègneFrance

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