Error analysis of digital filters realized with floating-point arithmetic

Abstract

This paper calculates the error at the output of a digital filter using floating-point arithmetic operations due to roundoff accumulation and input quantization. Expressions are derived for the mean square error for each of the three canonical forms of realization: direct, cascade, and parallel. Upper bounds that are useful for a special class of filters are given. The theoretical result is found to be in good agreement with the experimental result.