Linear Phase FIR Digital Filters with Cyclotomic Resonators

This paper describes a design method of linear phase recursive FIR digital filters. The basic structure consists of a transversal part cascaded with a cyclotomic resonator, which is characterized by cycotomic polynomials and has no multipliers. The digital filters implemented by this method require the short wordlength both for multiplier coefficients and for signals in their transversal part. By introducing integer arithmetic, the filtering operation proceeds fast and exactly. As a bonus, it is possible to employ a multiplier-less implementation in most practical applications. While the stability of this type of structure requires an integer-valued impulse response, a satisfactory procedure assures the requirement. A parameter to control the approximation error is found somewhat predictively rather than tentatively