A separation theorem for finite precision digital filters

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. Here we extend this proposition to the important case in which the input need not be zero and a certain more general type of arithmetic is used