A more commonly encountered representation of filter phase response is called the group delay, defined by
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 . 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.