Optimal rational approximation of bandpass Butterworth filter with symmetric fractional-order roll-off

Abstract In this paper, a fractional-order bandpass Butterworth filter (FBPBF) exhibiting symmetric roll-off characteristic is approximated as an integer-order transfer function using a metaheuristic optimization approach. A novel cost function is proposed by considering the exact FBPBF magnitude characteristic obtained through cascading the ( n + α ) , where n is an integer and 0 α 1 , order lowpass and highpass Butterworth filter responses. Design examples considering various values of n and α are presented to illustrate the performance efficacy of the proposed approach. PSPICE simulations for the models realized using the current feedback operational amplifiers confirm proximity to the theoretical characteristics.