采用改进遗传算法优化FIR数字滤波器设计

FIR数字滤波器的最优化设计可以抽象成一个多维连续函数求极值的问题，因此可以采用遗传算法求解。针对传统遗传算法存在的容易早熟收敛的问题，提出一种改进策略，从交叉变异的概率和算子两方面对算法进行改进，并通过测试函数验证了改进策略的可行性。分别在最小二乘（LS）、最大误差最小化（MM）和均方误差最小化（MMSE）准则下，采用改进遗传算法进行FIR数字低通滤波器最优化设计，实验结果显示在不同优化准则下设计的滤波器都表现出了良好的性能，证明了改进算法的通用性和有效性。

Research on design of FIR filter based on improved genetic algorithm

The optimal design of finite impulse response filter can be abstracted into a problem of calculating the extremum of multidimensional continuous function, so it can be solved by genetic algorithm. Because the traditional genetic algorithm is easy to fall into local solution, it proposes a new strategy to improve the algorithm in the probability and operator of crossover and mutation, and it proves to be feasible by trial function. Under the Least Squares（LS）, Minimax（MM） and Minimum Mean Square Error（MMSE） criteria, it realizes the optimized design of digital FIR low pass filters based on the improved genetic algorithm. The experimental results show that the filters designed under different optimality criteria have good performance, and the versatility and effectiveness of the improved genetic algorithm are proved as well.