Field programmable analogue array implementation of fractional step filters

Abstract

In this study, the authors propose the use of field programmable analogue array hardware to implement an approximated fractional step transfer function of order (n+α) where n is an integer and 0 < α < 1. The authors show how these filters can be designed using an integer order transfer function approximation of the fractional order Laplacian operator sα. First and fourth-order low- and high-pass filters with fractional steps from 0.1 to 0.9, that is of order 1.1–1.9 and 4.1–4.9, respectively, are given as examples. MATLAB simulations and experimental results of the filters verify the implementation and operation of the fractional step filters.