Closed-Form Design of Variable Fractional Order Integrator Using Complex Cepstrum

In this paper, the design problem of variable fractional order integrator (FOI) is investigated. First, the transfer function of FOI is obtained by taking fractional power of the transfer function of conventional first order integrator. Then, to implement this irrational transfer function, the complex cepstrum and Taylor series expansion are used to get a realizable approximated rational function. The proposed implementation structure is similar to the conventional Farrow structure of fractional sample delay filter. Finally, the design of variable fractional Simpson integrator is demonstrated to illustrate the performance of the proposed method.