IMPROVED FINITE WORD-LENGTH CHARACTERISTICS IN DIGITAL-CONTROL USING DELTA-OPERATORS

Some of the consequences of finite word lengths in digital control are examined. It is shown that in many cases of practical importance, (i. e. , when the shift operator poles are closer to 1 plus jo than to the origin), the usual shift operator formulation is inferior to an alternative formulation which is designated the delta operator approach. This latter approach is shown to give better coefficient representation and less roundoff noise in many cases. Thus the authors argue that the shift operator and its associated Z-transform can be replaced by delta operators and their associated transform which is designated a DELTA -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.