Publication result detail

Fractional-order band-pass filter design using fractional-characteristic specimen functions

KUBÁNEK, D.; FREEBORN, T.; KOTON, J.

Original Title

Fractional-order band-pass filter design using fractional-characteristic specimen functions

English Title

Fractional-order band-pass filter design using fractional-characteristic specimen functions

Type

WoS Article

Original Abstract

Two (α + β)-order transfer functions realizing fractional-order band-pass filter responses are presented and analysed, where 0 < α ≤ 1 and 0 < β ≤ 1. Generalizing the transfer functions from integer to fractional order offers continuous and independent control of the magnitude characteristic slopes both below and above the filter center frequency. The transfer function coefficients that minimize the magnitude error between the discussed fractional-order transfer functions and proposed fractional-characteristic specimen functions in a specified frequency band are determined using a numerical least squares optimization search routine. The relations for computing the transfer function coefficients as functions of α and β are given. The simulations show that the magnitude frequency characteristics of the transfer functions with the new coefficients are very well matched with the specimen functions. Further verification of these results was carried out using the Tow-Thomas filter topology with RC approximations of fractional-order capacitors. The computation of filter element parameters is demonstrated for selected values of α and β and the simulated and measured frequency characteristics of the filter are included to validate the fractional-order responses.

English abstract

Two (α + β)-order transfer functions realizing fractional-order band-pass filter responses are presented and analysed, where 0 < α ≤ 1 and 0 < β ≤ 1. Generalizing the transfer functions from integer to fractional order offers continuous and independent control of the magnitude characteristic slopes both below and above the filter center frequency. The transfer function coefficients that minimize the magnitude error between the discussed fractional-order transfer functions and proposed fractional-characteristic specimen functions in a specified frequency band are determined using a numerical least squares optimization search routine. The relations for computing the transfer function coefficients as functions of α and β are given. The simulations show that the magnitude frequency characteristics of the transfer functions with the new coefficients are very well matched with the specimen functions. Further verification of these results was carried out using the Tow-Thomas filter topology with RC approximations of fractional-order capacitors. The computation of filter element parameters is demonstrated for selected values of α and β and the simulated and measured frequency characteristics of the filter are included to validate the fractional-order responses.

Keywords

Fractional-order filter; Fractional calculus; Band-pass filter; Transfer function; Magnitude response

Key words in English

Fractional-order filter; Fractional calculus; Band-pass filter; Transfer function; Magnitude response

Authors

KUBÁNEK, D.; FREEBORN, T.; KOTON, J.

RIV year

2020

Released

01.04.2019

Publisher

ELSEVIER SCI LTD

Location

England

ISBN

0026-2692

Periodical

MICROELECTRONICS JOURNAL

Volume

2019

Number

86

State

United Kingdom of Great Britain and Northern Ireland

Pages from

77

Pages to

86

Pages count

10

URL

https://doi.org/10.1016/j.mejo.2019.02.020

BibTex

@article{BUT157947,
  author="David {Kubánek} and Todd {Freeborn} and Jaroslav {Koton}",
  title="Fractional-order band-pass filter design using fractional-characteristic specimen functions",
  journal="MICROELECTRONICS JOURNAL",
  year="2019",
  volume="2019",
  number="86",
  pages="77--86",
  doi="10.1016/j.mejo.2019.02.020",
  issn="0026-2692",
  url="https://doi.org/10.1016/j.mejo.2019.02.020"
}