(New page: == Sampling Theorem == Let <math>\omega_m</math> be a non-negative number. Let <math>x(t)</math> be a signal with <math>X(\omega) = 0</math> when <math>|\omega| > \omega_m</math>. Consi...) |
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Consider the samples <math>x(nT)</math> for <math>n = 0, +-1, +-2, ...</math> | Consider the samples <math>x(nT)</math> for <math>n = 0, +-1, +-2, ...</math> | ||
| − | If <math>T < \frac{1}{2}(\frac{2\pi}{\omega_m})</math> then <math>x(t)</math> can be uniquely recovered from its | + | If <math>T < \frac{1}{2}(\frac{2\pi}{\omega_m})</math> then <math>x(t)</math> can be uniquely recovered from its samples. |
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| + | == Variable Definitions == | ||
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| + | <math>T</math> Sampling Period | ||
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| + | <math>\frac{2\pi}/T = \omega_s</math> Sampling Frequency | ||
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| + | <math>T < \frac{1}{2}(\frac{2\pi}{\omega_m}) <==> \omega_s>2\omega_m</math> | ||
Revision as of 11:11, 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 $
