Direct Digital Fractional-Order Butterworth Filter Design using Constrained Optimization

Abstract This paper deals with the optimal design of digital fractional-order Butterworth filter (DFOBF) of order (n+α), where n is an integer and α ∈ (0, 1), using a single-step, discretization operator-free approach. Two distinct design routes are presented to realize the infinite impulse response (IIR) type DFOBFs with guaranteed stability and minimum-phase response. The first technique is based on constrained optimization, where the design constraints are explicitly formulated as inequality relations. In contrast, the second method is based on the pole-zero optimization, which uses the variable boundary constraints to meet the same objectives. Extensive comparisons regarding the modelling accuracy, solution robustness, and computational efficiency are conducted for the design of IIR-DFOBFs of orders two to five, for various values of n and α. Results reveal the superiority of the constrained optimization technique in producing accurate and robust solution quality. Comparisons with the reported literature also validate the improved performance of the proposed technique.