A new method for estimating derivatives based on a distribution approach

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.