Improvement of IIR Filter Discretization for Fractional Order Filter by Discrete Stochastic Optimization

Abstract

Fractional calculus has many implications for the field of signal processing, particularly in filter design. Fractional order filter functions are generalization of all rational filter structures including integer-order filter functions and it provides more options in term of frequency selectivity property. This study presents application of stochastic optimization methods for the improvement of IIR filter discretization of fractional order continuous filter structures. We used results of well-known fractional order discretization methods as initial filter model and improved the amplitude response of discrete filter for a better fitting to the continuous fractional-order filters. Illustrative examples demonstrate that it is possible to further improve amplitude responses of IIR filter discretization obtained for the fractional order differentiators, the first and second order continuous fractional-order filter structures by using basic random search algorithms. Digital filter design is very essential for digital signal processing applications and findings of this paper may contribute to digital filter design field in practice.