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 N_q samples is


where rho is the normalized correlation coefficient


For rho<<1,

 SNR approx rhosqrt(N_q).

The identical result is obtained for oversampling. For undersampling, the signal-to-noise ratio decreases (Thompson et al. 1986).

See also

Nyquist Sampling, Oversampling, Quantization Efficiency, Sample, Sample Size, Sampling Theorem, Shah Function, Sinc Function

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Feuer, A. Sampling in Digital Signal Processing and Control. Boston, MA: Birkhäuser, 1996.Govindarajulu, Z. Elements of Sampling Theory and Methods. Upper Saddle River, NJ: Prentice-Hall, 1999.Thompson, A. R.; Moran, J. M.; and Swenson, G. W. Jr. Interferometry and Synthesis in Radio Astronomy. New York: Wiley, pp. 214-216, 1986.

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Cite this as:

Weisstein, Eric W. "Sampling." From MathWorld--A Wolfram Web Resource.

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