Recursive realizations of n‐th order fir filters with linear phase designed by (n‐1) point frequency sampling technique

Abstract In determining approximately impulse responses of linear‐phase Nth‐order FIR filters by the N‐point frequency sampling method, the approximated impulse response is expressed as a sum of cosine or sine function series with phase shift corresponding to half series time width having sampled values as coefficients. On the other hand, the (N‐1) point frequency sampling method enables one to obtain the approximated impulse response in a form of a sum of cosine or sine function series without phase shift having sampled values as coefficients. In the recursive realization of triangular function series, the triangular function series without phase shift can be realized using a smaller number of multipliers than the triangular function series with phase shift. The (N‐1) point frequency sampling provides more effective recursive realization than the N‐point frequency sampling. If the normal form is used, the number of multipliers can be reduced by 33% and the processing speed and round‐off noise can be improved considerably.