Shift Operator
The shift operator is defined by
and

denotes the entire shifted
signal. Note that
since indexing is modulo

, the shift is
circular (or
``cyclic''). However, we normally use it to represent
time
delay by

samples. We often use the shift operator in
conjunction with
zero padding (appending zeros to the signal

, §
7.2.7) in order to avoid the ``wrap-around''
associated with a circular shift.
Figure 7.2:
Successive one-sample shifts of a
sampled periodic sawtooth waveform having first period
.
![\includegraphics[width=\twidth]{eps/shift}](http://www.dsprelated.com/josimages_new/mdft/img1153.png) |
Figure 7.2 illustrates successive one-sample delays of a periodic signal
having first period given by
.
-
(an impulse delayed one sample).
-
(a circular shift example).
-
(another circular shift example).
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