In statistics, sampling is the selection and implementation of statistical observations in order to estimate properties of an underlying population. Sampling is a vital part of modern polling, market research, and manufacturing, and its proper use is vital in the functioning of modern economies. The portion of a population selected for analysis is known as a sample, and the number of members in the sample is called the sample size.
The term "sampling" is also used in signal processing to refer to measurement of a signal at discrete times, usually with the intension of reconstructing the original
signal. For infinite-precision sampling of a band-limited signal at the Nyquist
frequency, the signal-to-noise ratio after 
samples is
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(1)
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(2)
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(3)
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where 
is the normalized correlation
coefficient
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(4)
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For 
,
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(5)
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The identical result is obtained for oversampling. For undersampling, the signal-to-noise ratio decreases (Thompson et al. 1986).
