应用差分进化算法的频率抽样法线性相位非递归数字滤波器设计

Design of Frequency Sampling Method based Linear Phase Non-recursive Digital Filters Using Differential Evolution Algorithm

滤波器过渡带最佳抽样点值的确定是频率抽样法非递归数字滤波器设计的关键,提出一种应用差分进化算法的频率抽样法线性相位非递归数字滤波器的优化设计方法。首先推导频率抽样法线性相位非递归数字滤波器的设计公式,并分析滤波器频率响应的误差特征。然后以滤波器过渡带样本值为优化变量,以阻带性能指标设计目标适应度函数,利用差分进化算法的全局性和内在并行性搜索最优解,并给出算法实现的具体步骤和实验结果。实验数据表明:采用差分进化算法确定的频率过渡带样点值是最优的,设计的非递归数字滤波器的通带最大衰减和阳带最小衰减分别达到0.2234 dB和66.6637 dB频率特性优干传统设计方法。

How to determine the optimal sampling point value of the filter transition band samples is a key problem in the design of non-recursive digital filters based on frequency sampling method(FSM).In this paper,an optimaloptimization design method using differential evolution algorithm(DEA) for FSM-based linear phase non-recursive digital filters is proposed.First of all,the design formulae of linear phase non-recursive digital filters based on FSM are derived,and the error features of the frequency responses of the designed filters are analyzed.And then the value of the transition band samples is utilized as the variable to be optimized,the objective fitness function is designed with the stopband performance specification,and the optimal solution is searched out by taking advantage of the globality and the intrinsic parallelism of DEA.Finally,the concrete steps and experimental results of the algorithm are presented.The experimental data show that the value of the frequency transition band samples determined by DEA is optimal,and the maximum passband attenuation and the stopband minimum stopband attenuation of the designed non-recursive digital filters can reach0.2234 dB and 66.6637 dB respectively,which are superior to other traditional design methods.