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IEVref:103-03-05ID:
Language:enStatus: 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 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaaiaadIhacqGH9aqpju gqbiaaicdaaaa@38BA@ , 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 2, 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 x0 of the variable x. The usual notation is:

f( x 0 )= + δ(x x 0 )f(x)dx MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWaamGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iEamaaBaaaleaajugWaiaaicdaaSqabaGccaGGPaGaeyypa0Zaa8qm aeaaimaacqWF0oazcaGGOaGaamiEaiabgkHiTiaadIhadaWgaaWcba qcLbmacaaIWaaaleqaaaqaaiaayIW7cqGHsislcqGHEisPaeaacaaM i8Uaey4kaSIaeyOhIukaniabgUIiYdGccaGGPaGaamOzaiaacIcaca WG4bGaaiykaKqzaeGaciizaOGaamiEaaaa@5364@

Figure 1 – Distribution de Dirac

Figure 1 – Dirac function


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
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