Tradeoff between roundoff and overflow errors in digital filter realizations

This paper is concerned with a linked analysis of overflow and roundoff errors in fixed-point digital filter realizations. Upper bounds for the overflow error power are obtained, having considered the saturation quantizer characteristics. Also, upper bounds for the overflow probability are given in order that the overflow power is lower than the roundoff noise power. Finally, computer simulation results support the theoretical ones, and some of these results are presented in curves for the optimal state-space digital realizations of Butterworth, Chebyshev and elliptic filters.