Step-invariant transform from z- to s-domain: a general framework

The conversion from discrete-time to continuous-time models is sometimes quite troublesome. This paper answers related pending questions concerning z-domain poles at the origin, and relating them to s-domain models with time delay. Special attention is devoted to the trade-off between fractional delay and direct feed-through. The paper places these questions into a general framework of model mapping between z-domain transfer functions and s-domain transfer functions, maybe with input delay. An algorithm to convert z-domain models with a pole at the origin is explained. A MATLAB routine has been implemented. The routine allows to execute the conversion either by defining the delay or the allowable direct feed-through. This routine is made available through the WWW.