Uncorrelated error properties of digital filters

In the implementation of digital filters, whether it be hardware or software implementation, registers consisting of a number of a finite number of bits are used to represent and manipulate quantities. A consequence of the use of this finite number of bits in the representation of quantities is the need for the roundoff of quantities after arithmetic or other operations. Round-off of the quantities results in errors, and the nature of these errors depends upon a variety of factors. In particular these errors are deterministic or stochastic depending upon whether the input is deterministic or stochastic, respectively. However, under certain circumstances for the case of the deterministic input, a stochastic model for the errors may be considered. This enables one to dichotomize the roundoff and other errors depending upon the correlated or the uncorrelated nature of these errors. The present paper considers various sources and the nature of these errors, and analyzes the generation, propogation and the effect of these errors on the performance of a digital filter, where the assumption of uncorrelatedness holds.