That is, for the normalized DFT (§6.10), the power
theorem becomes simply
(Normalized DFT case)
We see that the power theorem expresses the invariance of the inner
product between two signals in the time and frequency domains. If we
think of the inner product geometrically, as in Chapter 5,
then this result is expected, because and are merely
coordinates of the same geometric object (a signal) relative to two
different sets of basis signals (the shifted impulses and the
normalized DFT sinusoids).
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