(→Variable Definitions) |
|||
| Line 14: | Line 14: | ||
<math>T</math> Sampling Period | <math>T</math> Sampling Period | ||
| − | <math>\frac{2\pi} | + | <math>\frac{2\pi}{T} = \omega_s</math> Sampling Frequency |
<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> | ||
Revision as of 11:13, 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 $
