Motivation

Estimating the derivatives of noisy signals is of paramount importance in many fields of engineering and applied mathematics. It is, however, a longstanding ill-posed and challenging problem, in the sense that a small error in measurement data can induce a significant error in the estimated derivatives.

Figure 1 shows the results of the numerical estimation of the first time derivative of a noisy signal based on an algebraic differentiator on the one hand and the simple difference quotient rule on the other. This simulation shows the excellent performance of this numerical differentiation approach.

Figure 1. Numerical differentiation of a noisy signal using a simple difference quotient on the one hand and an algebraic differentiator on the other.