Definition: The shift operator is defined by
and denotes the entire shifted signal. Note that since indexing is modulo , the shift is circular. 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 ) in order to avoid the “wrap-around” associated with a circular shift.
Figure 8.2:Successive one-sample shifts of a sampled periodic sawtooth waveform having first period .
Figure 8.2 illustrates successive one-sample delays of a periodic signal having first period given by .
Example: (an impulse delayed one sample).
Example: (a circular shift example).
Example: (another circular shift example).