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<math>x(t)\!</math> -------> x --------> <math>x_p(t)\!</math> | <math>x(t)\!</math> -------> x --------> <math>x_p(t)\!</math> | ||
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^ | ^ | ||
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<math>p(t) = \sum^{\infty}_{n = -\infty} \delta(t - nT)\!</math> | <math>p(t) = \sum^{\infty}_{n = -\infty} \delta(t - nT)\!</math> | ||
Revision as of 12:45, 9 November 2008
Impulse-train Sampling
One type of sampling that satisfies the Sampling Theorem is called impulse-train sampling. This type of sampling is achieved by the use of a periodic impulse train multiplied by a continuous time signal, $ x(t)\! $. The periodic impulse train, $ p(t)\! $ is referred to as the sampling function, the period, $ T\! $, is referred to as the sampling period, and the fundamental frequency of $ p(t)\! $, $ \omega_s = \frac{2\pi}{T}\! $, is the sampling frequency. We define $ x_p(t)\! $ by the equation,
Graphically, this equation looks as follows,
$ x(t)\! $ -------> x --------> $ x_p(t)\! $
^ | |
$ p(t) = \sum^{\infty}_{n = -\infty} \delta(t - nT)\! $
