### Repeat Operator

Like the and operators, the operator maps a length signal to a length signal:

**Definition: **The *repeat times* operator is defined for any
by

^{7.10}An example of is shown in Fig.7.8. The example is

A frequency-domain example is shown in Fig.7.9. Figure 7.9a shows the original spectrum , Fig.7.9b shows the same spectrum plotted over the unit circle in the plane, and Fig.7.9c shows . The point (dc) is on the right-rear face of the enclosing box. Note that when viewed as centered about , is a somewhat ``triangularly shaped'' spectrum. We see three copies of this shape in .

The repeat operator is used to state the Fourier theorem

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Downsampling Operator

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Interpolation Operator