**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
*2017-09-28* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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## Rayleigh Energy Theorem (Parseval’s Theorem)

Theorem:For any ,

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

normalizedDFT.