Sampling-time effects of higher-order digitisations and their applications in digital redesign

Abstract

A study is made of the sampling-time effects of higher-order digitisations (i.e. the Madwed and Boxer-Thaler digitisations) to convert a continuous-time system into a discrete-time system. A general expression for the denominator and numerator of the digitised system is proposed, and used to predict precisely the computational stability and sampling-time effects of these types of digitisation. The 'polynomial root locus' is introduced to describe the pole variations of the digitised system when the sampling time is varied from zero to infinity. The maximum sampling time of a particular digitisation can also be found by a new algorithm which is proposed. The transient behaviour of the digitised system is further studied by defining a new set of transient terms for discrete-time systems. In this way, the effects of sampling-time can be studied thoroughly. It is shown that the appropriate sampling times obtained via these approximate methods play a meaningful role in selecting appropriate sampling times for real problems. Several examples are illustrated.