Randomized regression in differentiators

Differentiation of a signal is required in many applications in the field of signal processing. Linear differentiators fail to give good results for signals corrupted by both Gaussian and impulsive type of noise. For such cases nonlinear methods can be used in order to obtain better results. In this paper we propose a method, which we call randomized regression differentiator, based on random sampling and giving very good results in the presence of Gaussian and impulsive types of noise. We also present a modification of this general method which is designed for piecewise linear signals and utilizes random samplings of one window position in the next one. The output of this differentiator has sharp transitions when the slope value changes and the constant slope areas are smooth having only few small deviations around the correct slope value.