The architecture of the allpass-based notch filter is shown in
Fig. 3.14. It consists of a series connection of
allpass filters with a feed-around. Thus, the delay line of the
flanger is replaced by a string of allpass filters. (A delay line is
of course an allpass filter itself.) The phaser will have a notch
wherever the phase of the allpass chain is at (180 degrees). It
can be shown that these frequencies occur very close to the resonant
frequencies of the allpass chain.
It is therefore convenient to use a
single conjugate pole pair in each allpass section, i.e., use
second-order allpass sections of the form
and is the radius of each pole in the complex-conjugate pole pair,
and pole angles are
. The pole angle can be interpreted as
where
is the resonant frequency and
is the sampling interval.