### 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 illustrates successive one-sample delays of a periodic signal having first period given by .

#### Examples

• (an impulse delayed one sample).

• (a circular shift example).

• (another circular shift example).

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