Delay approximation for synchronous filter topologies

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