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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 [51, pp. 274-5].


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[How to cite this work] [Order a printed hardcopy]

``Mathematics of the Discrete Fourier Transform (DFT), with Music and Audio Applications'', by Julius O. Smith III, W3K Publishing, 2003, ISBN 0-9745607-0-7.
Copyright © 2007-02-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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