Signal differentiation by means of algebraic techniques and sliding mode techniques

The numerical differentiation has been considered an important problem to deal in control, signal processing, applied mathematics, among others. Several techniques based on Luenberger observers, homogeneity, algebraic techniques have been developed considering the problems that can be associated to a real signal. In this manuscript, a qualitative study was made to show the behavior of different differentiation techniques. The differentiation algorithms were based mainly in the algebraic techniques and polynomial approximation. A second approach was selected as the well known homogeneous differentiator. Four different differentiator techniques were studied: the algebraic differentiator, a di§erentiator based on Legendre polynomials, a differentiator based on Jacobi polynomials and the Homogeneous differentiator. The problems inherit to signal di§erentiation included in the analysis are the algorithm complexity and algorithm accuracy under noise and quantisation