Length limit of optimal finite wordlength FIR filters

Abstract

In practical FIR digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits. The optimal finite wordlength coefficients have an interesting property. For all finite wordlength filters there exists a maximum filter length Nmax and the corresponding cosine polynomial degree nmax. Increasing the filter length N beyond Nmax gives additional coefficients that are all zero. A theoretical explanation for the existence of Nmax is given in the paper. The influence of the filter specifications on Nmax is investigated. In addition, a simple method that gives a reasonably accurate estimate of Nmax is also given. Knowing Nmax and its relationship to the filter specifications is important in the finite wordlength FIR design because it can reduce the time needed to compute the optimal coefficients.