(→Sampling theorem) |
(→Sampling theorem) |
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| − | With sampling period | + | With sampling period T, samples of x(t),x(nT), can be obtained , where n = 0 +-1, +-2, .... |
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Wc has to exist between Wm and Ws-Wm. | Wc has to exist between Wm and Ws-Wm. | ||
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| + | Here is a diagram. | ||
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| + | x(t) ------> multiply ---------> <math>x_{p}(t)</math> | ||
| + | ↑ | ||
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| + | | | ||
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| + | <math> p(t) = \sum{\infty}_{-\infty}\delta(t-nT)</math> | ||
Revision as of 15:29, 9 November 2008
Sampling theorem
Here is a signal, x(t) with X(w) = 0 when |W| > Wm.
With sampling period T, samples of x(t),x(nT), can be obtained , where n = 0 +-1, +-2, ....
The sampling frequency is $ \frac{2\pi}{T} $. It is called Ws.
If Ws is greater than 2Wm, x(t) can be recovered from its samples.
Here, 2Wm is called the "Nyquist rate".
To recover, first we need a filter with amplited T when |W| < Wc.
Wc has to exist between Wm and Ws-Wm.
Here is a diagram.
x(t) ------> multiply ---------> $ x_{p}(t) $
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$ p(t) = \sum{\infty}_{-\infty}\delta(t-nT) $
