Discrete time is noncontinuous time. Sampling at noncontinuous times results in discretetime samples. For example, a newspaper may report the price of crude oil once every 24 hours. In general, the sampling period in discretetime systems is constant, but in some cases nonuniform sampling is also used.
Discretetime signals are typically written as a function of an index n (for example, x(n) or x_{n} may represent a discretisation of x(t) sampled every T seconds). In contrast to continuoustime systems, where the behaviour of a system is often described by a set of linear differential equations, discretetime systems are described in terms of difference equations. Most Monte Carlo simulations utilize a discretetiming method, either because the system cannot be efficiently represented by a set of equations, or because no such set of equations exists. Transformdomain analysis of discretetime systems often makes use of the Z transform.
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One of the fundamental concepts behind discrete time is an implied (actual or hypothetical) system clock^{[1]}. If one wishes, one might imagine some atomic clock to be the de facto system clock.
Uniformly sampled discrete time signals can be expressed as the timedomain multiplication between a pulse train and a continuous time signal. This timedomain multiplication is equivalent to a convolution in the frequency domain. Practically, this means that a signal must be bandlimited to half the sampling frequency, F_{s}/2, in order to prevent aliasing. Likewise, all nonlinear operations performed on discretetime signals must be bandlimited to F_{s}/2.
Usage: when the phrase "discrete time" is used as a noun it should not be hyphenated; when it is a compound adjective, as when one writes of a "discretetime stochastic process", then, at least according to traditional punctuation rules, it should be hyphenated. See hyphen for more.

