Publication detail

Transfer Functions of Fractional-Order Band-Pass Filter with Arbitrary Magnitude Slope in Stopband

KUBÁNEK, D. FREEBORN, T. KOTON, J. DVOŘÁK, J.

Original Title

Transfer Functions of Fractional-Order Band-Pass Filter with Arbitrary Magnitude Slope in Stopband

English Title

Transfer Functions of Fractional-Order Band-Pass Filter with Arbitrary Magnitude Slope in Stopband

Type

conference paper

Language

en

Original Abstract

Four band-pass (BP) filter transfer functions of the fractional order 1 < (1 + α) < 2 are presented. Their coefficients are found using numerical least squares optimization that aims at minimizing the magnitude errors between these transfer functions and the specimen functions that correspond to 2nd-order Butterworth filter responses. The fractional-order (FO) BP transfer functions with the proposed coefficients and coefficients previously presented in the literature for Butterworth-like FO low-pass (LP) transfer functions are compared. This comparison highlights that using the coefficients determined for FO LP transfer functions in FO BP functions causes distorted characteristics in some cases. The FO BP functions with the proposed coefficients match the specimen functions very well reducing this distortion.

English abstract

Four band-pass (BP) filter transfer functions of the fractional order 1 < (1 + α) < 2 are presented. Their coefficients are found using numerical least squares optimization that aims at minimizing the magnitude errors between these transfer functions and the specimen functions that correspond to 2nd-order Butterworth filter responses. The fractional-order (FO) BP transfer functions with the proposed coefficients and coefficients previously presented in the literature for Butterworth-like FO low-pass (LP) transfer functions are compared. This comparison highlights that using the coefficients determined for FO LP transfer functions in FO BP functions causes distorted characteristics in some cases. The FO BP functions with the proposed coefficients match the specimen functions very well reducing this distortion.

Keywords

band-pass filter; fractional calculus; fractional-order filter; magnitude response; transfer function

Released

01.07.2019

Publisher

IEEE

Location

Budapest, Hungary

ISBN

978-1-7281-1864-2

Book

Proceedings of the 2019 42nd International Conference on Telecommunications and Signal Processing (TSP), Budapest, Hungary

Pages from

655

Pages to

659

Pages count

5

URL

BibTex


@inproceedings{BUT157946,
  author="David {Kubánek} and Todd {Freeborn} and Jaroslav {Koton} and Jan {Dvořák}",
  title="Transfer Functions of Fractional-Order Band-Pass Filter with Arbitrary Magnitude Slope in Stopband",
  annote="Four band-pass (BP) filter transfer functions of the fractional order 1 < (1 + α) < 2 are presented. Their coefficients are found using numerical least squares optimization that aims at minimizing the magnitude errors between these transfer functions and the specimen functions that correspond to 2nd-order Butterworth filter responses. The fractional-order (FO) BP transfer functions with the proposed coefficients and coefficients previously presented in the literature for Butterworth-like FO low-pass (LP) transfer functions are compared. This comparison highlights that using the coefficients determined for FO LP transfer functions in FO BP functions causes distorted characteristics in some cases. The FO BP functions with the proposed coefficients match the specimen functions very well reducing this distortion.",
  address="IEEE",
  booktitle="Proceedings of the 2019 42nd International Conference on Telecommunications and Signal Processing (TSP), Budapest, Hungary",
  chapter="157946",
  doi="10.1109/TSP.2019.8769089",
  howpublished="online",
  institution="IEEE",
  year="2019",
  month="july",
  pages="655--659",
  publisher="IEEE",
  type="conference paper"
}