Using New Hybrid Integrators to Design IIR Fractional-Order Integrators via Impulse Invariance Method

This paper presents a method for designing fullband and non-fullband IIR digital integrators with linear phase that has been used to approximate fractional-order integrators with IIR filters. Several numerical integration rules have been considered in this study, namely, Euler, Simpson, Schneider, bilinear, and F₀₁₂. The main idea in our design is based on interpolating the well-known integration rules (Euler, Bilinear and Simpson) proposed by Al-Alaoui combined with deterministic signal modeling techniques. Numerical examples are presented to illustrate the performance of the proposed integrators. It was found that the Euler–Simpson integrator gives better approximation accuracy than existing integrators.