In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values.

A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a reconstruction filter.

Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions.

For functions that vary with time, let ${\displaystyle s(t)}$ be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every ${\displaystyle T}$ seconds, which is called the sampling interval or sampling period. Then the sampled function is given by the sequence:

The sampling frequency or sampling rate, ${\displaystyle f_{s}}$, is the average number of samples obtained in one second, thus ${\displaystyle f_{s}=1/T}$, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second.

Reconstructing a continuous function from samples is done by interpolation algorithms. The Whittaker–Shannon interpolation formula is mathematically equivalent to an ideal low-pass filter whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant ${\displaystyle (T)}$, the sequence of delta functions is called a Dirac comb. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with ${\displaystyle s(t)}$. That mathematical abstraction is sometimes referred to as impulse sampling.

Most sampled signals are not simply stored and reconstructed. The fidelity of a theoretical reconstruction is a common measure of the effectiveness of sampling. That fidelity is reduced when ${\displaystyle s(t)}$ contains frequency components whose cycle length (period) is less than 2 sample intervals (see Aliasing). The corresponding frequency limit, in cycles per second (hertz), is ${\displaystyle 0.5}$ cycle/sample × ${\displaystyle f_{s}}$ samples/second = ${\displaystyle f_{s}/2}$, known as the Nyquist frequency of the sampler. Therefore, ${\displaystyle s(t)}$ is usually the output of a low-pass filter, functionally known as an anti-aliasing filter. Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process.