2nd vs 1st order all pass filter

Started by May 27, 2013
Given that the magnitude response of a first order all pass filter is perfectly flat, what reasons are there to consider a filter greater than one order? Presumably it is to do with varying the phase in a different way, but can anyone give me a good real world application?
With an analog implementation, there is a trade-off between
the amount of group delay you can get and the frequency range over which the
group delay will be relatively constant.  Higher order all-pass filters will provide a constant specified group delay over
a wider range of frequencies.  Of course,
with a digital implementation you can theoretically get a constant delay over
an infinite range of frequencies.  See
the following:
T Kugelstadt  “Active
Filter Design Techniques”
Douglas Self  “The
Design of Active Crossovers” Chapter 10 (Not Available online.)