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 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).