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Time-Limited Signals

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

$\displaystyle \Delta t\cdot\Delta \omega \geq \pi$ (B.69)

where $ \Delta\omega$ is as defined above in (B.62).



Proof: See [202, pp. 274-5].


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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