Roundoff noise in state-space digital filtering: A general analysis

Abstract

A new noise expression is formulated for the class of fixed-point digital filters described by the state equations, and two methods of its computation are discussed. The effects of possible structure transformation and state-amplitude scalings are then incorporated in this expression, and the results have been analyzed. In particular, it is shown that the output noise and state amplitudes are inversely proportional, and that an elementary transformation is well suited for a step-by-step generation of a low-noise filter.