Digital fractional delay implementation based on fractional order system

This study presents a design method of the digital fractional delay operator z^-m for 0<;m<;1, in a given frequency band of interest, using digital infinite impulse response (IIR) filters. The design technique is based on the approximation of the fractional order systems. First, analogue rational function approximation, for a given frequency band, of the fractional power pole (FPP) is given. Then the forward difference generating function is used to digitise the FPP to obtain a closed-form IIR digital filter, which approximates the digital fractional delay operator z^-m for 0<;m<;1. Finally, an example is presented to illustrate the effectiveness of the proposed design method. The proposed technique has also been used to design a comb filter. The results obtained have been discussed and compared with some of the most recent work in the literature.