Allpass1 is a simple filter that transmits all frequencies
without affecting their amplitudes; however, the allpass filter delays
frequencies by different amounts according to the filter gain as can
be seen in the group delay
plot for this allpass filter. Note that if the gain g of the
filter is 0, then the delay amount for all frequencies is 1 sample.
Here is a flowgraph view of the first-order allpass filter:
The pole-zero diagram for the allpass filter below show the general
placement of poles and zeros for an allpass filter. Poles lie within
the unit circle and zeros are placed at the conjugate angle of the pole
with an inverse distance from the origin. For the Allpass1
filter, g can only be real, so the pole-zero pair can only
be found on the real axis. The magnitude of w along |z| = 1 (the
dashed circle) is constant.