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<math>T < \frac{1}{2}(\frac{2\pi}{\omega_m}) <==> \omega_s>2\omega_m</math> | <math>T < \frac{1}{2}(\frac{2\pi}{\omega_m}) <==> \omega_s>2\omega_m</math> | ||
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| + | <math>\omega_m</math> Maximum frequencye for a band limited signal | ||
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| + | <math>NQ = 2\omega_m</math> Nyquist Rate - The frequencye the sampling frequency should be, or greater. | ||
| + | |||
| + | <math>\omega_c = </math> | ||
Revision as of 11:21, 10 November 2008
Sampling Theorem
Let $ \omega_m $ be a non-negative number.
Let $ x(t) $ be a signal with $ X(\omega) = 0 $ when $ |\omega| > \omega_m $.
Consider the samples $ x(nT) $ for $ n = 0, +-1, +-2, ... $
If $ T < \frac{1}{2}(\frac{2\pi}{\omega_m}) $ then $ x(t) $ can be uniquely recovered from its samples.
Variable Definitions
$ T $ Sampling Period
$ \frac{2\pi}{T} = \omega_s $ Sampling Frequency
$ T < \frac{1}{2}(\frac{2\pi}{\omega_m}) <==> \omega_s>2\omega_m $
$ \omega_m $ Maximum frequencye for a band limited signal
$ NQ = 2\omega_m $ Nyquist Rate - The frequencye the sampling frequency should be, or greater.
$ \omega_c = $
