A new algorithm to obtain $\delta$-operator based transfer function from its continuous time counterpart

Abstract

This paper discusses the advantages of the $\delta$-operator over the forward shift operator q in implementation of discrete-time systems. The $\delta$-operator gives better coefficient representation and less round-off noise in many cases. As an application, a new algorithm is introduced here to obtain $\delta$-operator based transfer functions from continuous time counterparts. Finally, a fourth-order Butterworth low-pass filter is taken as an example to compare coefficient sensitivity effects of q- and $\delta$-operator systems.