Optimal design study of three-type FIR high-order digital filters based on sine basis functions neural-network algorithm

An optimal design approach of high-order FIR digital filter is developed based on the algorithm of neural networks which its activation matrix is produced by the sine basis functions. The main idea is to minimize the sum of the square errors between the amplitude-frequency response of the desired FIR filter and that of the designed by training the weight vector of sine basis functions neural networks, then obtains the impulse response of three-type FIR digital filter with linear phase. The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing two kinds of high-order FIR digital filters, i.e., band-pass and multi-band-pass filters. The results of the amplitude responses show that attenuation in stop-bands is more than 290 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of pass-bands and stop-bands is easily controlled precisely. The presented optimal design approach of high-order FIR digital filter is significantly effective.