A new fractional order recursive digital integrator using continued fraction expansion

Abstract

In this paper a new fractional order recursive digital integrator is presented. Fractional order integrators have a wide range of applications in automatic control systems, circuit theory, dynamical systems and signal processing. The implementation of fractional order recursive digital integrator requires two steps. In the first step, an integer order digital integrator is designed then in the next step continued fraction expansion (CFE) is used to obtain an efficient fractional order digital integrator which is suitable over the complete Nyquist frequency range. The proposed half order integrator accurately approximates the ideal half order integrator reasonably well over the entire Nyquist frequency range with absolute magnitude error ≤ 0.05 and it outperforms the existing half order integrators.