Power Theorem

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Power Theorem

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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Power Theorem



Theorem: For all $x,y\,

\

Proof:

\


Note that the power theorem would be more elegant ($\) if the DFT were defined as the coefficient of projection onto the normalized DFT sinusoid ${\.

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