Summary: The module looks at circular shifting and how it is can be used as a tool to represent the shifting of a periodic sequence.
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The many properties of the DFT become really straightforward (very similar to the Fourier Series) once we have once concept down: Circular Shifts.
We can picture periodic sequences as having discrete points on a circle as the domain
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Shifting by
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To cyclic shift we follow these steps:
1) Write
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2) To cyclic shift by
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If
It's called circular shifting, since we're moving around the circle. The usual shifting is called "linear shifting" (shifting along a line).
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If
"My introduction to signal processing course at Rice University."