# Discrete Time

Discrete time is the discontinuity of a function's time domain that results from sampling a variable at a finite interval. For example, consider a newspaper that reports the price of crude oil once every day at 6:00AM. The newspaper is described as sampling the cost at a frequency of 24 hours, and each number that's published is called a sample. The price is not defined by the newspaper in between the times that the numbers were published. Suppose it is necessary to know the price of the oil at 12:00PM on one particular day in the past; one must base the estimate on any number of samples that were obtained on the days before and after the event. Such a process is known as interpolation. 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 signal 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.

### Other articles related to "discrete time, discrete, time":

Discrete Time - 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 ... Likewise, all non-linear operations performed on discrete-time signals must be bandlimited to Fs/2 - ε ...
Linear-quadratic-Gaussian Control - Mathematical Description of The Problem and Solution - Discrete Time
... Since the discrete-time LQG control problem is similar to the one in continuous-time the description below focuses on the mathematical equations ... Discrete-time linear system equations Here represents the discrete time index and represent discrete-time Gaussian white noise processes with covariance matrices respectively ... The quadratic cost function to be minimized The discrete-time LQG controller , The Kalman gain equals, where is determined by the following matrix Riccati difference equation that runs forward in time, The ...
LTI System Theory - Overview
... properties of any LTI system are linearity and time invariance ... Time invariance means that whether we apply an input to the system now or T seconds from now, the output will be identical except for a time delay of the T ... Hence, the system is time invariant because the output does not depend on the particular time the input is applied ...
Stochastic Control - Discrete Time
... In a discrete time context, the decision-maker observes the state variable, possibly with observational noise, in each time period ... sum of expected values of a nonlinear (possibly quadratic) objective function over all the time periods from the present to the final period of concern, or to optimize the value of the objective ... At each time period new observations are made, and the control variables are to be adjusted optimally ...
Linear-quadratic Regulator - Infinite-horizon, Discrete-time LQR
... For a discrete-time linear system described by with a performance index defined as the optimal control sequence minimizing the performance index is given by ...

### Famous quotes containing the words time and/or discrete:

At the same time that we are earnest to explore and learn all things, we require that all things be mysterious and unexplorable, that land and sea be infinitely wild, unsurveyed and unfathomed by us because unfathomable.
Henry David Thoreau (1817–1862)

The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.
W.V. Quine (b. 1908)