Delay approximation for synchronous filter topologies

It is shown that the original definition of e developed by Euler can be use d as the basis of a delay approximation where all the pales have the same v alue. Furthermore, it is demonstrated that by splitting the Euler function into complex pole pairs, by the addition of an artificial variable beta, an additional degree of freedom can be introduced. Through optimisation of th e value of beta it is shown that either the group delay or step response ca n be optimised. This delay approximation, when compared to a standard Besse l approximation, is shown to provide acceptable performance for many applic ations. Furthermore, it offers the considerable practical benefit of being realisable as a cascade of identical building block elements when appropria te technologies (e.g. second-order active filter blocks) are used.