Improved finite word length characteristics in digital control using delta operators

This paper examines some of the consequences of finite word lengths in digital control. It is shown that, in many cases of practical importance, the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach. This latter approach is shown to give better coefficient representation and less roundoff noise in many cases. We thus argue that the shift operator and its associated <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</tex> -transform can be replaced by delta operators and their associated transform which we designate a Δ-transform. An added advantage of this approach is that discrete designs and transforms converge to their continuous-time counterparts as the sampling rate is increased.