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Encyclopedia > 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. 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. 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. In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In mathematics, a recurrence relation, also known as a difference equation, is an equation which defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. ... Monte Carlo methods are a class of computational algorithms for simulating the behavior of various physical and mathematical systems. ... In mathematics and signal processing, the Z-transform converts a discrete time domain signal, which is a sequence of real numbers, into a complex frequency domain representation. ...

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. Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ... For the computer science usage see convolution (computer science) . In mathematics and in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version... Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. ... A bandlimited signal is a deterministic or stochastic signal (e. ... In statistics, signal processing, and related disciplines, aliasing is an effect that causes different continuous signals to become indistinguishable (or aliases of one another) when sampled. ...

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. In the mathematics of probability, a stochastic process is a random function. ... A hyphen ( -, or â€ ) is a punctuation mark. ...

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 Discrete - Wikipedia, the free encyclopedia (275 words) In topology, a branch of mathematics, a discrete space is a topological space in which all sets are open, and a discrete set is a set of isolated points. In discrete mathematics, without notion of continuity, a discrete set is a countable set; this concept is also important for combinatorics, probability theory, and statistical theory. In discrete mathematics and in theoretical computer science, the abstract world is usually modeled as a discrete space with discrete time.
 Discrete time - definition of Discrete time in Encyclopedia (272 words) 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). Uniformly sampled discrete time signals can be expressed as the time-domain multiplication between a pulse train and a continuous time signal. 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.
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