Time-Limited Signals
If for
, then
![$\displaystyle \Delta t\cdot\Delta \omega \geq \pi
$](http://www.dsprelated.com/josimages_new/mdft/img1761.png)
![$ \Delta \omega $](http://www.dsprelated.com/josimages_new/mdft/img1762.png)
![$ \,$](http://www.dsprelated.com/josimages_new/mdft/img131.png)
Proof: See [52, pp. 274-5].
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Time-Bandwidth Products are Unbounded Above
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Duration and Bandwidth as Second Moments
If for
, then
Proof: See [52, pp. 274-5].