Optimal Design on FIR Digital Filters Using the Parallel Algorithm of Neural Networks

This paper introduces in detail the optimal design approach of high-order FIR digital filter and differentiator using the algorithm of neural networks. The main idea is to minimize the sum of the square errors between the amplitude response of the ideal FIR digital filter or digital differentiator and that of the designed by training the weight vector of neural networks, then obtaining the impulse response of FIR digital filter or differentiator. The convergence theorem of the neural-network algorithm is presented and proved, and the optimal design approach is introduced by examples of high-order FIR digital filter and digital differentiator. The results show that the high-order FIR digital filter or digital differentiator designed by training the weights of neural networks has a very high precision and very fast convergence speed, and initial weights are stochastic. Therefore, the presented optimum design method in the paper is significantly effective