Rayleigh Energy Theorem (Parseval's Theorem)

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Rayleigh Energy Theorem (Parseval's Theorem)

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Rayleigh Energy Theorem (Parseval’s Theorem)



Theorem: For any $x\,

\

I.e.,

\

Proof: This is a special case of the Power Theorem.

Note that again the relationship would be cleaner ($\) if we were using the normalized DFT.

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