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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 nonuniform sampling is also used.

Discrete-time signals are typically written as a function of an index n (for example, x(n) or xn may represent a discretisation of x(t) sampled every T seconds). 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. Most Monte Carlo simulations utilize a discrete-timing method, either because the system cannot be efficiently represented by a set of equations, or because no such set of equations exists. Transform-domain analysis of discrete-time systems often makes use of the Z transform.

Contents

System clock

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.

Time signals

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 be 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.

Notes

  1. ^ "... digital systems [...] usually are discretized in time (there is a system clock)", Gershenfeld 1999, p.18

References

  1. Gershenfeld, Neil A. (1999). The Nature of mathematical Modeling. Cambridge University Press. ISBN 0 521 57095 6.  

See also








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