The allpass filter passes all frequencies with equal gain. This
is in contrast with a lowpass filter, which passes only low
frequencies, a highpass which passes high-frequencies, and a bandpass
filter which passes an interval of frequencies. An allpass filter may
have any phase response. The only requirement is that its amplitude
response be constant. Normally, this constant is
.
From a physical modeling point of view, a unity-gain allpass filter
models a lossless system in the sense
that it preserves signal energy. Specifically, if
denotes the input to an allpass filter
, and if
denotes
its output, then we have
Appendix C proves that Eq.(B.9) holds if and only if
That is, a filter