In practice, a signal may be said to be linear phase
when its phase is of the form
where
![$ \Delta$](http://www.dsprelated.com/josimages_new/mdft/img1144.png)
is any real constant (usually an integer), and
![$ I(\omega_k)$](http://www.dsprelated.com/josimages_new/mdft/img1380.png)
is an
indicator function which takes on the
values 0 or
![$ 1$](http://www.dsprelated.com/josimages_new/mdft/img111.png)
over the points
![$ \omega_k$](http://www.dsprelated.com/josimages_new/mdft/img677.png)
,
![$ k=0,1,2,\ldots,N-1$](http://www.dsprelated.com/josimages_new/mdft/img887.png)
.
An important class of examples is when the signal is regarded as a
filter impulse response.
7.14 What all such
signals have in common is that they are
symmetric about the time
![$ n=\Delta$](http://www.dsprelated.com/josimages_new/mdft/img1381.png)
in the time domain
(as we will show on the next page). Thus, the term ``linear phase
signal'' often really means ``a signal whose phase is linear between
![$ \pm\pi$](http://www.dsprelated.com/josimages_new/mdft/img1361.png)
discontinuities.''
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