The analytical approach for designing bandpass FIR filters by frequency sampling method

The problem of designing bandpass FIR filters by frequency sampling method in case of one frequency sample (transition coefficient) in each transition band is considered. The analytical expressions for calculating these samples are obtained. Samples are calculated on the basis of criterion of minimum of the sum of squared frequency response values in selected points in the stopband. In the general case values of transition coefficients are calculated to be unequal. It is demonstrated that in this case the higher attenuation level in the stopband is achieved in the comparison with the case of transition coefficient values equality. The results of digital modeling shows that obtained expressions allow achieving attenuation, which is close to maximum.