Discrete time and continuous time: Difference between revisions

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{{Short description|Frameworks for modeling variables that evolve over time}}

{{redirect-distinguish|Discrete signal|Discrete variable}}

In [[Dynamical system|mathematical dynamics]], '''discrete time''' and '''continuous time''' are two alternative frameworks within which to model [[Variable (mathematics)|variables]] that evolve over time.

In [[Dynamical system|mathematical dynamics]], '''discrete time''' and '''continuous time''' are two alternative frameworks within which to model [[Variable (mathematics)|variables]] that evolve over time are modeled.

==Discrete time==

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==Continuous time==

In contrast, '''continuous time''' views variables as having a particular value only for potentially only an [[infinitesimal]]ly short amount of time. Between any two points in time there are an [[infinity|infinite]] number of other points in time. The variable "time" ranges over the entire [[real number line]], or depending on the context, over some subset of it such as the non-negative reals. Thus time is viewed as a [[continuous variable]].

A '''continuous signal''' or a '''continuous-time signal''' is a varying [[quantity]] (a [[signal (information theory)|signal]])

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A typical example of an infinite duration signal is:

:<math>f(t) = \sin(t), \quad t \in \mathbb{R}</math>

A finite duration counterpart of the above signal could be:

:<math>f(t) = \sin(t), \quad t \in [-\pi,\pi]</math> and <math>f(t) = 0</math> otherwise.

The value of a finite (or infinite) duration signal may or may not be finite. For example,

:<math>f(t) = \frac{1}{t}, \quad t \in [0,1]</math> and <math>f(t) = 0</math> otherwise,

is a finite duration signal but it takes an infinite value for <math>t = 0\,</math>.