Optimal Design Study of High-Order FIR Digital Filters Based on Neural-Network Algorithm

This paper traverses the optimal design approach of high order FIR digital filters based on the parallel algorithm of neural networks, which its activation matrix is produced by cosine basis functions. The main idea is to minimize the sum of the square errors between the amplitude response of the desired FIR filter and that of the designed by training the weight vector of neural networks, then obtaining the impulse response of FIR digital filter. The convergence theorem of the neural-network parallel algorithm is presented and proved, and the optimal design approach is introduced by examples of 2000th order FIR digital filters. The results of the amplitude responses show that attenuation in stop-band is more than 230 dB with no ripple and pulse existing in pass-band, and cutoff frequency of pass-band and stop-band is easily controlled precisely. Therefore, the presented optimal design approach of high order FIR digital filters is significantly effective