It is clear that this ideal transfer function can not be approached by
any classical series development since 0 is a singular value for
. As in many DSP applications, we care much about the
behaviour of the filter at low frequency rather than at high
frequency. Moreover low frequencies are mapped in the z-plane into
the neighborhood of 1. We shall demonstrate that the different
low-frequency approximations for the ideal FDDF (expressed as
maximally flat delay approximations around the null frequency)
corresponds to different kind of Padé approximations of
around z=1, i.e approximations of 
around x=0 with
.