Design of FIR and IIR fractional order Simpson digital integrators

In this paper, the design of fractional order Simpson digital integrator is investigated. First, the conventional transfer function of second-order IIR Simpson integrator is factorized into product of first-order factors. Then, each factor of product is fractionalized by taking fractional power and using binomial series expansion. Next, truncating the length of series expansion, the transfer functions of FIR and IIR fractional order Simpson integrators are obtained. It is shown that the IIR fractional integrator is always stable. Finally, design examples are demonstrated to illustrate the performance of the proposed method and some further improvement using fractional delay is also discussed.