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== Impulse-train Sampling == | == 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, <math>x(t)\!</math>. The periodic impulse train, <math>p(t)\!</math> is referred to as the sampling function, the period, <math>T\!</math>, is referred to as the sampling period, and the fundamental frequency of <math>p(t)\!</math>, <math>\omega_s = \frac{2\pi}{T}\!</math>, is the sampling frequency. We define <math>x_p(t)\!</math> by the equation, | 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, <math>x(t)\!</math>. The periodic impulse train, <math>p(t)\!</math> is referred to as the sampling function, the period, <math>T\!</math>, is referred to as the sampling period, and the fundamental frequency of <math>p(t)\!</math>, <math>\omega_s = \frac{2\pi}{T}\!</math>, is the sampling frequency. We define <math>x_p(t)\!</math> by the equation, | ||
| − | <center><math>x_p(t) = x(t)p(t)\!</math></center> | + | <center><math>x_p(t) = x(t)p(t)\!</math>, where</center> |
| + | |||
| + | <center><math>p(t) = \sum^{\infty}_{n = -\infty}\!</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,
