Design of IIR digital fractional-order differ-integrators using closed-form discretization

This paper introduces a new design method of fractional-order IIR digital differentiators (FODD) and integrators (FODI) using a closed-form discretization technique. Unlike the direct or the indirect discretization methods that uses CFE to generate a digital differential or integral operators, which sometimes yield an unstable non-minimum phase digital filter, the proposed approach always yields a minimum phase stable rational z-transfer functions for both FODDs and FODIs. The significance of the proposed method lies in the simplicity of the design, which only depends on the fractional-order differentiator or the integrator. The main points of this work are illustrated via numerical examples.