基于改进差分进化算法的Ⅱ型频率采样法FIR数字滤波器设计

The Design of FIR Digital Filters Using Type-Ⅱ Frequency Sampling Method based on Modified Differential Evolution Algorithm

在传统差分进化算法的基础上,增加缩放因子自适应生成策略、交叉概率抛物线式动态产生策略和新个体基因边界检查和处理方法,提出一种改进差分进化算法并应用于采用Ⅱ型频率采样法的FIR数字滤波器设计中。该优化设计方法以滤波器过渡带样点值为优化变量,以阻带最小衰减值作为优化目标并设计适应度函数,利用改进差分进化算法的全局寻优能力求解最优样点值。文中结合FIR数字高通、低通和带通滤波器设计的3个例子,给出算法实现的具体步骤和实验结果。实验数据表明:采用改进差分进化算法确定的滤波器过渡带样点值是最优的,设计的FIR数字滤波器频响特性(通带最大波动和阻带最小衰减)优于传统查表方法和遗传算法。

On the basis of the traditional differential evolution(TDE)algorithm,an adaptive generation strategy for the scalar factor,a parabolic dynamic generation strategy for the crossover probability and a method for checking and processing the boundary of the new individual’s genes are added into the TDE algorithm.A modified differential evolution(MDE)algorithm is proposed accordingly and applied to the design of FIR digital filters using type-Ⅱfrequency sampling method.The sample values of the filters in the transition bands are taken as the optimization variables;the minimum stopband attenuation is used as the optimization objective to design the corresponding fitness function;the global excellent searching ability of the MDE algorithm are employed to solve the best sample values by this optimal design method.Three examples of the design of digital FIR based on high-pass,low-pass and band-pass filters are given in this paper,and the detailed procedures and experimental results of the implementation of the algorithm are also presented.The experimental data have shown that the sample values of the filters in the transition bands determined by the MDE algorithm are optimal,and the frequency response characteristics(maximum passband ripple and minimum stopband attenuation)of the FIR digital filters designed are superior to the traditional look-up table method and genetic algorithm.