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
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is the normalized correlation
coefficient
 |
(4)
|
For 
,
 |
(5)
|
The identical result is obtained for oversampling. For undersampling, the signal-to-noise ratio decreases (Thompson et al. 1986).
