Delay approximation for synchronous filter topologies

摘要

It is shown that the original definition of e developed by Eulerncan be used as the basis of a delay approximation where all the polesnhave the same value. Furthermore, it is demonstrated that by splittingnthe Euler function into complex pole pairs, by the addition of annartificial variable Β, an additional degree of freedom can benintroduced. Through optimisation of the value of Β it is shown thatneither the group delay or step response can be optimised. This delaynapproximation, when compared to a standard Bessel approximation, isnshown to provide acceptable performance for many applications.nFurthermore, it offers the considerable practical benefit of beingnrealisable as a cascade of identical building block elements whennappropriate technologies (e.g. second-order active filter blocks) arenused