A new method for estimating derivatives based on a distribution approach

Nathalie Verdière (1) , Lilianne Denis-Vidal (2) , Ghislaine Joly-Blanchard (2)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

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.

Mots clés: derivatives estimation; distributions; test functions

Domaines: Systèmes dynamiques [math.DS]

Nathalie Verdière, Lilianne Denis-Vidal, Ghislaine Joly-Blanchard. A new method for estimating derivatives based on a distribution approach. Numerical Algorithms, 2012, pp.Online first. ⟨10.1007/s11075-012-9535-4⟩. ⟨hal-00696672⟩