IEVref: | 103-03-05 | ID: | |

Language: | en | Status: Standard | |

Term: | Dirac function | ||

Synonym1: | Dirac delta function [Preferred] | ||

Synonym2: | unit pulse [Preferred] | ||

Synonym3: | unit impulse, US [Preferred] | ||

Symbol: | δ | ||

Definition: | distribution assigning to any function f(x), continuous for $x=0$, the value f(0)Note 1 to entry: The Dirac function can be considered as the limit of a function, equal to zero outside a small interval containing the origin, and the integral of which remains equal to unity when this interval tends to zero. See Figure 1, where instead of a triangle any other shape with area 1 is possible, too. Note 2 to entry: The Dirac function is the derivative of the unit step function considered as a distribution. Note 3 to entry: The Dirac function can be defined for any value $f({x}_{0})={\displaystyle {\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}\delta (x-{x}_{0}})f(x)\mathrm{d}x$
| ||

Publication date: | 2009-12 | ||

Source | |||

Replaces: | |||

Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO | ||

CO remarks: | |||

TC/SC remarks: | |||

VT remarks: | |||

Domain1: | |||

Domain2: | |||

Domain3: | |||

Domain4: | |||

Domain5: |

Note 1 to entry: The Dirac function can be considered as the limit of a function, equal to zero outside a small interval containing the origin, and the integral of which remains equal to unity when this interval tends to zero. See Figure 1, where instead of a triangle any other shape with area 1 is possible, too.

Note 2 to entry: The Dirac function is the derivative of the unit step function considered as a distribution.

Note 3 to entry: The Dirac function can be defined for any value *x*_{0} of the variable *x*. The usual notation is:

$f({x}_{0})={\displaystyle {\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}\delta (x-{x}_{0}})f(x)\mathrm{d}x$

**Figure 1 – Dirac function**