An Efficient Structure for Finite Precision Implementation of Digital Systems

This paper deals with optimal state-space realizations of digital systems implemented with finite word length (FWL). A pole modulus sensitivity based stability related measure is derived and the optimal realizations are defined as those that maximize the proposed measure. Based on a polynomial operator approach, a new sparse realization is developed. This is a very efficient structure containing some free parameters which provide more degrees of freedom to reduce the FWL effects. The problem of finding optimal sparse realizations is solved. Two numerical examples are given to illustrate the design procedure and to compare the performance of different realizations.