线性FIR滤波器的最优化方法.pdf

中国科技论文在线 线性FIR 滤波器的最优化方法 李玥东，李雅梅，何小双** （辽宁工程技术大学电气与控制工程学院，葫芦岛 125105 ） 5 摘要：在数字滤波器设计中，在同样的阶数下，等波纹最佳逼近的优化设计方法可以获得较 准确的截止频率，同时具有通带和阻带平坦过渡带窄等优点。加权Chebyshev 等波纹逼近基 本定理，交错定理，Parks-McCLellan 算法可以用来设计最优化线性相位FIR 滤波器。在运 算过程中，发现标准的Remez 算法非常复杂，本文提出一套递推计算公式，使得Remez 算 10 法变得直接，简单和明了。同时，为了提高经程序运行效率，我们认为在靠近过渡带的频率 区域，不均匀设置极值频率初始估计值；在通带的中间和阻带的中间，则均匀设置极值频率 初始估计值。 关键词：FIR 数字滤波器；Chebyshev 等波纹逼近算法；直接Remez 算法；交错定理 中图分类号：TN713+.7 15 The optimum design of FIR digital filter LI Yuedong, LI Yamei, HE Xiaoshang (School of Electrical and Control Engineering, Liaoning Technical University, Huludao 125105) Abstract: In the design of digital filters ，under the same order number, equiripple filter 20 optimization design method can obtain more accurate cut-off frequency, it has the advantages of gently pass band, attenuation band and narrow transition zone. Chebyshev ripple approximation fundamental theorem, interlaced theorem and Parks - McCLellan algorithm optimization can be used to design optimize linear phase FIR filter. In the process of operation, we found standard Remez algorithm is very complicated, the article puts forward a set of recursion formula which 25 makes Remez algorithm more directly, simple and clearer. At the same time, in order to improve the efficiency of the program, we should set extremum frequency initial estimates unequally; In the middle of the pass band and attenuation band, we set extremum frequency initial estimates equally. Key words: FIR DF; Chebyshev ripple approximation fundamental theorem; Directly Remez 30 algorithm; Intervening theorem 0 引言 [1] 数字滤波器