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Time-Limited Signals

If $ x(t)=0$ for $ \left\vert t\right\vert\geq \Delta t/2$ , then

$\displaystyle \Delta t\cdot\Delta \omega \geq \pi
$

where $ \Delta \omega $ is as defined above in Eq.$ \,$ (C.1).



Proof: See [54, pp. 274-5].


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``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 © 2014-04-21 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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