基于Oustaloup算法的分数高阶有源滤波器研究  

The Research of Higher Fractional-order Active Filter Based on Oustaloup's Algorithm

作　　者：王芳[1] 岳春光[1] 刘玉芳[1] 李丹[2] 

机构地区：[1]河南师范大学物理与信息工程学院,河南新乡453007 [2]中国电波传播研究所,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2012年第5期65-68,共4页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(60977063);河南省教育厅科技攻关项目(2010A510007)

摘　　要：在比较分析了连分数展开法和Oustaloup算法特点的基础上,提出了一种基于Oustaloup算法并利用电可调跨导运算放大器(EOTA)来实现的分数高阶有源滤波器设计方法.分数阶是用整数阶传递函数逼近分数阶拉普拉斯算子Sα的方法实现,0<α<1.将Oustaloup逼近算法用EOTA实现从而解决了连分数展开法的不稳定问题.仿真实现了α为2.2、2.5、2.8阶时的低通滤波器频率响应,通带内未出现尖峰,阻带内衰减误差小于2%,结果证实了理论分析的正确性,这为设计实现高精度有源滤波器提供了理论依据.Based on comparison of continued fraction expansions and the Oustaloup’s algorithm,we proposed a method of realizing higher fractional-order active filter based on Oustaloup’s algorithm,which was implemented by EOTA.We used integer-order transfer function approximation of the fractional-order Laplacian operator Sα,0〈α〈1.To solve the problem of instability of continued fraction expansion,We used EOTA to achieve Oustaloup to replace it.There was no peaking in passband and stop-band attenuation of less than 2% in the simulation of low-pass filter’s Frequency-Response when α was 2.2、2.5、2.8 respectively.We analysised the continued fraction expansions and the Oustaloup’s algorithm and achieving it by EOTA.Simulation results show the correctness of the theory,which provided a theoretical basis to realize high precision active filter design.

关 键 词：分数高阶有源滤波器 EOTA Oustaloup算法 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]