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 (a continuous signal) to a sequence of samples (a discrete-time signal).
A sample is a value or set of values at a point in time and/or space.
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.
Sampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions.
For functions that vary with time, let 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 T seconds, which is called the sampling interval or the sampling period. Then the sampled function is given by the sequence:
The sampling frequency or sampling rate, fs, is the average number of samples obtained in one second (samples per second), thus fs = 1/T.