The phase response
of an LTI filter gives the radian
phase shift experienced by each sinusoidal component of the input
signal. It is often more intuitive to consider instead the phase
delay, defined as

The phase delay gives the time delay in seconds experienced by
each sinusoidal component of the input signal. For example, in the
simplest lowpass filter of Chapter 1, we found that the phase response
was
, which corresponds to a phase
delay
, or one-half sample. Thus, we can say
precisely that the filter
exhibits half a sample of
time delay at every frequency. (Note that it is now obvious how we
should define the filter phase response at the degenerate frequencies
0 and .)