Approximate realization of digital fractional forward operator using digital IIR filter

Abstract

In this paper, a simple and an efficient approach for approximating the digital fractional forward operator zm (0 < m < 1) using digital infinite impulse response (IIR) filter is proposed. In this method, the coefficients of the closed form digital IIR filter derived for the approximation of the fractional forward operator, in a given frequency band, are based on approximation of fractional order systems. First, analog rational function approximation, in a given frequency band, of the fractional power zero (FPZ) is given. Then, the forward difference generating function is used to obtain a closed form IIR digital filter equivalent of the continuous FPZ, which approximates the digital fractional forward operator. Finally, illustrative examples have been presented to illustrate the effectiveness of the proposed design technique of the fractional forward operator zm approximation and its use in performing a fractional m-step prediction.