Research on Optimal Design of Fractional Order Lowpass Filters

HE Xue; HU Zhi-zhong

doi:10.12263/DZXB.20210019

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Research on Optimal Design of Fractional Order Lowpass Filters

PAPERS | 更新时间：2025-12-08

- Research on Optimal Design of Fractional Order Lowpass Filters
- ACTA ELECTRONICA SINICA Vol. 50, Issue 1, Pages: 185-194(2022)
- 作者机构：
  
  南京航空航天大学电子信息工程学院，江苏南京 211106
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20210019
  CLC： TN713;
- Received：24 December 2020，
  
  Revised：2021-03-08，
  
  Published：25 January 2022
- 稿件说明：
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何雪,胡志忠.分数阶低通滤波器的优化设计研究[J].电子学报,2022,50(01):185-194.

HE Xue,HU Zhi-zhong.Research on Optimal Design of Fractional Order Lowpass Filters[J].ACTA ELECTRONICA SINICA,2022,50(01):185-194.
何雪,胡志忠.分数阶低通滤波器的优化设计研究[J].电子学报,2022,50(01):185-194. DOI： 10.12263/DZXB.20210019.

HE Xue,HU Zhi-zhong.Research on Optimal Design of Fractional Order Lowpass Filters[J].ACTA ELECTRONICA SINICA,2022,50(01):185-194. DOI： 10.12263/DZXB.20210019.

摘要

分数阶滤波器由于具备连续步进的阻带衰减速率和更大的设计自由度而受到国内外学者的广泛关注.本文提出两种符合指标要求的分数阶低通滤波器的优化设计方法，即采用Matlab优化工具箱中的Fminimax和Fgoalattain两种多目标优化函数来分别设计符合指标要求的两种不同形式传递函数的分数阶低通滤波器，通过比较通带偏差、阻带偏差以及群时延等参数，总结这两种方法所优化设计的滤波器各自的特点.给出设计实例，对其进行稳定性分析和电路仿真，并搭建电路证明了所提设计方法的有效性.

Abstract

Fractional order filters have received extensive attention from scholars at home and abroad because of their continuous stepped stopband attenuation rate and greater design freedom. This paper proposes two optimization design methods for fractional order lowpass filters that meet the design specifications

that is

using two multi-objective optimization functions of Fminimax and Fgoalattain in the Matlab optimization toolbox to design fractional order lowpass filters with two different forms of transfer functions that meet the design specifications. By comparing parameters such as passband deviation

stopband deviation

and group delay

the characteristics of the filters optimized by the two methods are summarized. A design example is given

stability analysis and circuit simulation are carried out

and the circuit is built to prove the effectiveness of the proposed design methods.

关键词

Keywords

references

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