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

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