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<center><math>x_p(t) = x(t)p(t)\!</math>, where</center> | <center><math>x_p(t) = x(t)p(t)\!</math>, where</center> | ||
− | <center><math>p(t) = \sum^{\infty}_{n = -\infty}\!</math> | + | <center><math>p(t) = \sum^{\infty}_{n = -\infty} \delta(t - nT)\!</math> |
Revision as of 12:41, 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,