Applying the Z-transform for the static analysis of floating-point numerical filters

Abstract

Digital linear filters are used in a variety of applications (sound treatment, control/command, etc.), implemented in software, in hardware, or a combination thereof. For safety-critical applications, it is necessary to bound all variables and outputs of all filters. We give a compositional, effective abstraction for digital linear filters expressed as block diagrams, yielding sound, precise bounds for fixed-point or floating-point implementations of the filters.