A simple method of computing the input quantization and multiplication roundoff errors in a digital filter

A simple method of calculating the steady-state value of the variance of the output noise of a digital filter due to the input quantization noise or internally generated noise from product round-off is presented. The output noise is expressed as a sum of simpler terms belonging to one of four basic groups. Explicit expressions have been developed for rapid evaluation of these terms in the expansion. The method is illustrated by means of examples.