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
Highlights
The process of applying an electronic filter to remove unwanted frequency characteristics from an input signal is one of the most often used operations in signal processing
To evaluate the BP transfer functions, the magnitude characteristics of each response compared to the secondorder Butterworth BP transfer function are presented in Fig. 5 and Fig. 6
The simulated magnitude characteristics of the generated FO HP and BP transfer functions have been compared to the ideal Butterworth responses to evaluate the most appropriate case to realize a FO response that still approximates the Butterworth response after the transformation
Summary
The process of applying an electronic filter to remove unwanted frequency characteristics from an input signal is one of the most often used operations in signal processing. These filter circuits are integer order (i.e. 1st, 2nd, 3rd), but recently filter circuits with a fractional-order (FO) (i.e. non-integer orders, 1.1, 2.7, 6.4, etc.) have been introduced [1]–[10].
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