A separation theorem for finite-precision digital systems

Abstract

For models of zero-input direct-form digital filters implemented in fixed-point digital hardware it is known that if saturation arithmetic is used and stability holds when the quantization is ignored, then the amplitude of all limit cycles can be made arbitrarily small by making the bound on the magnitude of the quantization sufficiently small. In that sense the effects of quantization and overflow can be considered separately. Recently, this proposition was extended to the case in which the input need not be zero. Here we give a result to the effect that quantization and overflow can be considered separately for a much more general class of discrete-time systems, and we give as an example an application of this result to systems governed by state equations.