(New page: This page will talk about the important property of sampling theorem. Consider the samples <math>x(nT)</math> for n = 0,-1,1,-2,2,... if <math>T < \frac{1}{2} \left (\frac{2\pi}{w_m} \ri...) |
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Consider the samples <math>x(nT)</math> for n = 0,-1,1,-2,2,... | Consider the samples <math>x(nT)</math> for n = 0,-1,1,-2,2,... | ||
| − | if <math>T < \frac{1}{2} \left (\frac{2\pi}{w_m} \right )\,</math> | + | if |
| + | |||
| + | :<math>T < \frac{1}{2} \left (\frac{2\pi}{w_m} \right )\,</math> | ||
| + | |||
| + | then <math>x(t)</math> can be uniquely recovered from its samples. In this case, T is the sampling period, and <math>\frac{2\pi}{T}</math> (or <math>w_s</math>) is the sampling frequency. | ||
| + | |||
| + | The important fact is that | ||
| + | |||
| + | :<math>T < \frac{1}{2}\frac{2\pi}{w_m}</math> | ||
| + | |||
| + | :<math>2w_m < \frac{2\pi}{T}</math> | ||
| + | |||
| + | but we mentioned before that <math>w_s = \frac{2\pi}{T}</math> therefore, | ||
| + | |||
| + | :<math>2w_m < w_s</math> | ||
| + | |||
| + | In which <math>2w_m</math> is called the Nyquist rate. | ||
Latest revision as of 15:28, 10 November 2008
This page will talk about the important property of sampling theorem.
Consider the samples $ x(nT) $ for n = 0,-1,1,-2,2,...
if
- $ T < \frac{1}{2} \left (\frac{2\pi}{w_m} \right )\, $
then $ x(t) $ can be uniquely recovered from its samples. In this case, T is the sampling period, and $ \frac{2\pi}{T} $ (or $ w_s $) is the sampling frequency.
The important fact is that
- $ T < \frac{1}{2}\frac{2\pi}{w_m} $
- $ 2w_m < \frac{2\pi}{T} $
but we mentioned before that $ w_s = \frac{2\pi}{T} $ therefore,
- $ 2w_m < w_s $
In which $ 2w_m $ is called the Nyquist rate.
