神经网络设计二维带通三型FIR滤波器

Designing of 2-D band-pass FIR filters of type-3

为了改善传统方法设计的二维带通三型有限脉冲响应(FIR)滤波器的幅频响应性能,提出了复合正弦基神经网络算法.以理想滤波器的幅度响应作为学习样本,通过复合正弦基神经网络训练,使得实际滤波器的幅度响应逼近理想滤波器的幅度响应,再由神经网络的权值得到滤波器的脉冲响应.给出了复合余弦基神经网络模型,建立了滤波器幅频响应与该神经网络的关系,同时指出了学习率对神经网络收敛性的影响,推导并证明了使该算法收敛的收敛定理.仿真结果表明,由该算法设计的二维带通三型FIR滤波器性能接近于理想滤波器,并且克服了传统神经网络的主要缺陷,收敛速度快.

For improving the magnitude and frequency response performance of 2-D bandpass finite impulse response （FIR） type-3 filters designed by the conventional algorithms, an compound-sine-basis neural network algorithm was proposed. By using the magnitude response of idea filters as training samples, the compound-sine-basis neural network made the filter magnitude response approach that of the ideal filter, and then the filter impulse response was obtained with neural network weights. The model of compound-sine-basis neural network was presented, and the relationships of the magnitude and frequency response and the neural network were derived. The training rate effects on the neural network convergence were pointed out, and the convergence theorem ensuring the algorithm to converge was given and proved. The results indicate that the performances of filters designed by the proposed algorithm are near those of ideal filters, and that the algorithm overcomes the main defects of conventional neural networks and increases the convergence speed.