is called a linear phase term is
that its phase is a linear function of frequency:
Thus, the slope of the phase, viewed as a linear function of
radian-frequency , is . In general, the time
delay in samples equals minus the slope of the linear phase
term. If we express the original spectrum in polar form as
where and are the magnitude and phase of , respectively
(both real), we can see that a linear phase term only modifies the spectral
. A positive time delay (waveform shift to
the right) adds a negatively sloped linear phase to the original
spectral phase. A negative time delay (waveform shift to the left) adds a
positively sloped linear phase to the original spectral phase. If we
seem to be belaboring this relationship, it is because it is one of the
most useful in practice.
Definition: A signal is said to be a linear phase signal if its phase
is of the form
where is any real constant, and
indicator function which takes on the values 0 or over the
A zero-phase signal is thus a linear phase signal for which the
phase-slope is zero.
As mentioned above (in §7.4.3), it would be more precise to
say ``piecewise constant phase'' instead of ``zero phase''.
Similarly, ``linear phase'' is better described as ``linear phase
interrupt by discontinuities.''