# Discrete time

Discrete time is non-continuous time. Sampling at non-continuous times results in discrete-time samples. For example, a newspaper may report the price of crude oil once every 24 hours. In general, the sampling period in discrete-time systems is constant, but in some cases non-uniform sampling is also used.

In contrast with continuous-time signals, where t is often the variable used for time, n is most commonly used with discrete-time signals (e.g., x(n) is the discretized signal x(t) sampled every nT seconds were T is the sampling period). In contrast to continuous-time systems, where the behaviour of a system is often described by a set of linear differential equations, discrete-time systems are described in terms of difference equations. Transform-domain analysis of discrete-time systems often makes use of the Z transform.

Uniformly sampled discrete time signals can be expressed as the time-domain multiplication between a pulse train and a continuous time signal. This time-domain multiplication is equivalent to a convolution in the frequency domain. Practically, this means that a signal must be bandlimited to half the sampling frequency, Fs/2, in order to prevent aliasing. Likewise, all non-linear operations performed on discrete-time signals must be bandlimited to Fs/2.

Usage: when the phrase "discrete time" is used as a noun it should not by hyphenated; when it is a compound adjective, as when one writes of a "discrete-time stochastic process", then, at least according to traditional punctuation rules, it should be hyphenated. See hyphen for more.

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