A more commonly encountered representation of filterphase response is
called the group delay, defined by

For linear phase responses, i.e.,
for
some constant , the group delay and the phase delay are
identical, and each may be interpreted as time delay (equal to
samples when
). If the phase response
is nonlinear, then the relative phases of the sinusoidal signal
components are generally altered by the filter. A nonlinear phase
response normally causes a ``smearing'' of attack transients such as
in percussive sounds. Another term for this type of phase distortion
is phase dispersion. This can be seen below in §7.10.5.

An example of a linear phase response is that of the simplest lowpass
filter,
. Thus, both the phase delay and the group
delay of the simplest lowpass filter are equal to half a sample at
every frequency.

For any phase function, the group delay may be interpreted
as the time delay of the amplitude envelope of a sinusoid at
frequency [62]. The bandwidth of the amplitude
envelope in this interpretation must be restricted to a frequency
interval over which the phase response is approximately linear.
We derive this result in the next subsection.

Thus, the name ``group delay'' for refers to the fact that
it specifies the delay experienced by a narrow-band ``group'' of
sinusoidal components which have frequencies within a narrow frequency
interval about . The width of this interval is limited to
that over which is approximately constant.