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.
Read more about Discrete Time: System Clock, Time Signals
Famous quotes containing the words discrete and/or time:
“One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one element after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.”
—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)
“If youth is the period of hero-worship, so also is it true that hero-worship, more than anything else, perhaps, gives one the sense of youth. To admire, to expand one’s self, to forget the rut, to have a sense of newness and life and hope, is to feel young at any time of life.”
—Charles Horton Cooley (1864–1929)