[1]孙 颖,刘 清,杨 涛.FIR滤波器的约束最小二乘设计[J].南京师范大学学报(工程技术版),2007,07(01):018-21.
　Sun Ying,Liu Qing,Yang Tao.Constrained Least Square Method Applied in FIR Filter Design[J].Journal of Nanjing Normal University(Engineering and Technology),2007,07(01):018-21.
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FIR滤波器的约束最小二乘设计
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南京师范大学学报（工程技术版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
07卷
期数:
2007年01期
页码:
018-21
栏目:
出版日期:
2007-03-30

文章信息/Info

Title:
Constrained Least Square Method Applied in FIR Filter Design
作者:
孙 颖1;  刘 清1;  杨 涛2
1. 南京师范大学数学与计算机科学学院, 江苏南京210097;
2. 解放军理工大学通信工程学院, 江苏南京210007
Author(s):
Sun Ying1; Liu Qing1; Yang Tao2
1.School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China;2.Institute of Communication Engineering,PLAUST,Nanjing 210007,China
关键词:
约束最小二乘;  FIR滤波器;  设计
Keywords:
constra ined least square;  FIR filter;  design
分类号:
TN713
摘要:
低通滤波常用在图像去噪中,抑制噪声从而改善图像质量.在应用中图像的处理要求不能有明显的相位失真,所以选用FIR滤波器,因为它在一定的对称条件下可实现严格的线性相位.FIR滤波器的设计最终可归结为求解一组滤波器系数,采用最小二乘法优化这些系数.为了对带有一些频域等式约束的FIR低通滤波器进行良好的设计,在最小二乘的基础上结合拉格朗日法.先将带约束的最小二乘转为求条件极值,引入拉格朗日乘子法构造出拉格朗日函数,再进行求解.最后进行了仿真实验,并比较了用一般遗传算法对FIR低通滤波器的设计.结果证明了这种方法的有效性.
Abstract:
Low pass filter is always used in restra in ing no ises o f im age and im prov ing the im ag e qua lities. In app lication, to ensure the linear phase o f im ag e, FIR filter is usua lly chosen as it can rea lize the str ict linea r phase under the conditions. Designing FIR filer actua lly m eans so lv ing a group of fine coe fficien ts. In th is paper, constra ined least squarem ethod is applied to design FIR low pass filter. In o rder to find good so lution to FIR filter w ith som e equation restrictions, the least square algor ithm is comb ined w ith Lag rang em ethod. First, transfo rm the least square question into a condition-extremum question w hich can be solved by Lag range m ethod. Then construc t the Lagrange function and ge t the so lution. Th is m ethod is proved effic ient by simu lating and compar ing w ith the gene tic a lgo rithm.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 孙 颖( 1981-) , 女, 硕士研究生, 主要从事图像处理等方面的学习与研究. E-m ail:w interbabe@ sohu. com
通讯联系人: 刘 清( 1962-) , 博士, 副教授, 主要从事智能控制与现场总线测控系统的研究与开发. E-m ail: n jnu lq@ 163. com
更新日期/Last Update: 2013-04-29