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Power Theorem


The inner product of two signals is defined as:

$\displaystyle \left<x,y\right> \;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;\sum_{n}x_n\overline{y}_n
$

Using this notation, we have the following:

$\displaystyle \zbox{\left<x,y\right> = \frac{1}{N} \left<X,Y\right>}
$




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``Review of the Discrete Fourier Transform (DFT)'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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