On minimisation of word length of multidimensional filter realisations

In this paper, we present a statistical word length minimisation procedure based on the dynamical model of stable-unstable transitions in N-dimensional digital filters. This dynamical model [1] was originally used to determine a priori, for a worst case design, the minimum word length of the multipliers needed to retain stability. In this contribution, the dynamical model of stable-unstable transitions in N-dimensional filters is used to estimate each multiplier´s minimum word length sufficient, in some statistical sense, to retain stability. The new procedure has been compared with the worst case procedure. It has been found that the present procedure results in a significant saving of the word length in comparison with the worst case analysis. The method is therefore an attractive alternative to the worst case procedure. Numerical examples are solved at the end to illustrate the procedure presented.