Some Effects of Quantization and Adder Overflow on the Forced Response of Digital Filters
Alan N. Willson · Bell System Technical Journal · 1972
The effects of quantization (i.e., roundoff, truncation, etc.) and adder overflow, which are present in any special-purpose computer type realization of a digital filter, cause an otherwise linear system to become quite nonlinear. Moreover, the presence of such nonlinearities can cause the system's response to differ drastically from the ideal response (that is, from the response of the linear model of the filter) even when the level of the filter's input signal is, in a certain reasonable sense, small, and when the quantization effects are made arbitrarily small. In this paper we derive a criterion for the satisfactory behavior of second-order digital filters in the presence of such nonlinear effects. The criterion is shown to be sharp, in that we also present a procedure for constructing counterexamples which show that, for most filters which violate the criterion, the response to some “small” nonzero input signal is not always even asymptotically close to the ideal response.