Shift Operator
The shift operator is defined by
and
![$ \hbox{\sc Shift}_{\Delta}(x)$](http://www.dsprelated.com/josimages_new/mdft/img1143.png)
denotes the entire shifted
signal. Note that
since indexing is modulo
![$ N$](http://www.dsprelated.com/josimages_new/mdft/img35.png)
, the shift is
circular (or
``cyclic''). However, we normally use it to represent
time
delay by
![$ \Delta$](http://www.dsprelated.com/josimages_new/mdft/img1144.png)
samples. We often use the shift operator in
conjunction with
zero padding (appending zeros to the signal
![$ x$](http://www.dsprelated.com/josimages_new/mdft/img25.png)
, §
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).
Next Section: ConvolutionPrevious Section: Flip Operator