Like the and operators, the operator maps a length signal to a length signal:
Definition: The repeat times operator is defined for any by
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