复系数FIR数字滤波器的神经网络设计方法

Design of FIR Filters in Complex Domain by Neural Networks

神经网络是一种设计实系数FIR滤波器的有效算法,为了将该方法扩展到复数域,建立统一的基于神经网络的滤波器设计框架,文中提出了一种用多层神经网络设计任意幅频响应的复系数FIR数字滤波器的新算法,主要思想是将设计问题转化为实系数多层神经网络的训练问题,在实数域对幅频响应的平方误差函数的实部和虚部分别进行最小化,误差将收敛到全局最小点。实验结果表明,利用该算法设计的滤波器具有较小的幅频响应误差和群延迟误差。该算法能解决具有任意幅频响应和群延迟要求的问题,是一种有效的设计算法。

This paper proposes a new algorithm based on multilayer neural networks for complex coefficients FIR digital tilters design with arbitrary amplitude-frequency response. The main idea is to solve the design problem by training multilayer neural networks in real domain ,then minimize the real part and imaginary part of squared - error function of amplitude response in real domain respectively. As a result a unique framework is developed for designing real and complex coefficients FIR filters. The simulation results show that the filters designed by proposed algorithm have tiny amplitude error and group delay error so this algorithm can solve the application problems with special requirement on amplitude and group delay.