Design of Digital Fractional-Order Integrators and Differentiators by Least Squares

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

In this paper we develop a method for obtaining digital rational approximations (IIR filters) to fractional-order operators of type sα, where α ∈ . The proposed method is based on the least-squares (LS) minimization between the impulse responses of the digital fractional-order integrator/differentiator and of the rational-fraction approximation. The results reveal that the LS approach gives similar or superior approximations in comparison with other methods. The effectiveness of the method is demonstrated both in the time and frequency domains through an illustrative example.