分数阶低通滤波器的优化设计研究  

Research on Optimal Design of Fractional Order Lowpass Filters

作　　者：何雪 胡志忠[1] HE Xue;HU Zhi-zhong(College of Electronic and Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing,Jiangsu 211106,China)

机构地区：[1]南京航空航天大学电子信息工程学院,江苏南京211106

出　　处：《电子学报》2022年第1期185-194,共10页Acta Electronica Sinica

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.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 optimiza⁃tion 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 pass⁃band deviation,stopband deviation,and group delay,the characteristics of the filters optimized by the two methods are sum⁃marized.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：分数阶微积分 分数阶滤波器 优化设计 

分 类 号：TN713[电子电信—电路与系统]