Evaluation of (1 + α) Fractional-Order Approximated Butterworth High-Pass and Band-Pass Filter Transfer Functions
Keywords:Active filters, Butterworth approximation, Fractional calculus, Fractional-order filters, Transfer functions.
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.
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