Publication detail

Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

MAHATA, S. HERENCSÁR, N. KUBÁNEK, D.

Original Title

Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters

Type

journal article in Web of Science

Language

English

Original Abstract

In this paper, a new two-steps design strategy is introduced for the optimal rational approximation of the fractional-order Butterworth filter. At first, the weighting factors of the summation between the nth -order and the (n+1)th -order Butterworth filters are optimally determined. Subsequently, this model is employed as an initial point for another optimization routine, which minimizes the magnitude-frequency error relative to the (n+α)th -order, where α∈(0,1) , Butterworth filter. The proposed approximant demonstrates improved performance about the magnitude mean squared error compared to the state-of-the-art design for six decades of bandwidth, but the introduced approach does not require a fractional-order transfer function model and the approximant of the sα operator. The proposed strategy also avoids the use of the cascading technique to yield higher-order fractional-order Butterworth filter models. The performance of the proposed 1.5th-order Butterworth filter in follow-the-leader feedback topology is verified through SPICE simulations and its hardware implementation based on Analog Devices AD844AN-type current feedback operational amplifier.

Keywords

Analog filter approximation, approximation method, Butterworth filter, current feedback operational amplifier, fractional calculus, fractional-order filter, interpolation, low-pass filter, mean square error method, optimization method.

Authors

MAHATA, S.; HERENCSÁR, N.; KUBÁNEK, D.

Released

2. 6. 2021

Publisher

IEEE

ISBN

2169-3536

Periodical

IEEE Access

Year of study

9

Number

1

State

United States of America

Pages from

81097

Pages to

81114

Pages count

18

URL

https://ieeexplore.ieee.org/document/9445054

Full text in the Digital Library

http://hdl.handle.net/11012/200668

BibTex

@article{BUT172046,
  author="Shibendu {Mahata} and Norbert {Herencsár} and David {Kubánek}",
  title="Optimal Approximation of Fractional-Order Butterworth Filter Based on Weighted Sum of Classical Butterworth Filters",
  journal="IEEE Access",
  year="2021",
  volume="9",
  number="1",
  pages="81097--81114",
  doi="10.1109/ACCESS.2021.3085515",
  issn="2169-3536",
  url="https://ieeexplore.ieee.org/document/9445054"
}