Evaluation of (1 + α) Fractional-Order Approximated Butterworth High-Pass and Band-Pass Filter Transfer Functions

Abstract

This paper summarizes multiple cases of high-pass (HP) and band-pass (BP) analogue filter transfer functions with fractional order 1 < (1 + α) < 2. All HP and BP transfer functions are evaluated against the magnitude characteristics of ideal Butterworth responses when coefficients previously determined to approximate fractional-order (FO) Butterworth low-pass (LP) transfer functions are utilized. Comparisons of the simulated FO HP and BP responses against the ideal Butterworth responses are presented, with a least squares error analysis applied to determine the transfer functions that best approximate the Butterworth response for both HP and BP FO filters. DOI: http://dx.doi.org/10.5755/j01.eie.24.2.20634

Keywords

• active filters
• butterworth approximation
• fractional calculus
• fractional-order filters
• transfer functions.