Optimal design study of high order FIR digital filters based on neural network algorithm

An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function. 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 weights of neural networks, then obtains the impulse response of FIR digital filter. The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing four kinds of FIR digital filters, i. e., low-pass, high-pass, bandpass, and band-stop FIR digital filter. The results of the amplitude responses show that attenuation in stop-bands is more than 60 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of passband and stop-band is easily controlled precisely. The presented optimal design approach of high order FIR digital filter is significantly effective.