Brief Contribution to Geometrical Theory of Zeroes and Poles of Bifractional Filters

Abstract

This paper briefly contributes to synthesis of non-integer order frequency filters. Well known method of construction of desired frequency responses based on locations of zeroes and poles is generalized to fractional-order (FO) domain. Several prototypes of FO transfer functions are geometrically interpreted using a complex plane. Each transfer function has a single real degree of freedom and corresponding unique frequency responses. Proposed approach is verified by example of very simple two-band FO audio equalizer.