(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled)Examples




IEVref:351-45-20ID:
Language:enStatus: Standard
Term: unit impulse
Synonym1: Dirac impulse
[Preferred]
Synonym2:
Synonym3:
Symbol: δ(t)
Definition: distribution, defined as the limit of a positive function, equal to zero outside a small interval containing the origin, the integral of which remains equal to one when this interval tends to zero

δ(t)={ 0 0 fort<0 fort=0 fort>0 with + δ(t) dt=1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meaabaGacmGadiWaaiWabaabaiaafaaake aaimaacqWF0oazcaGGOaGaamiDaiaacMcacqGH9aqpdaGabaqaauaa beqadeaaaeaacaaIWaaabaGaeyOhIukabaGaaGimaaaaaiaawUhaau aabeqadeaaaeaacaaMe8UaaeiCaiaab+gacaqG1bGaaeOCaiaaysW7 caWG0bGaeyipaWJaaGimaaqaaiaaysW7caqGWbGaae4Baiaabwhaca qGYbGaaGjbVlaadshacqGH9aqpcaaIWaaabaGaaGjbVlaabchacaqG VbGaaeyDaiaabkhacaaMe8UaamiDaiabg6da+iaaicdaaaGaaGzbVl aabggacaqG2bGaaeyzaiaabogadaWdXbqaaiab=r7aKjaacIcacaWG 0bGaaiykaaWcbaGaeyOeI0IaeyOhIukabaGaey4kaSIaeyOhIukani abgUIiYdGccaaMe8UaciizaiaadshacqGH9aqpcaaIXaaaaa@751C@

SEE: Figure 4a) and IEC 60027-6.

Note 1 to entry: A distribution assigns a number to any function f(t), sufficiently smooth for t = t0 [see CEI 60050-103:2009, 103-03-05].

The Dirac impulse does this according to

f( t 0 )= δ ( t t 0 )f( t )dt MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaqadaqaaiaadshadaWgaaWcbaGaaGimaaqabaaakiaawIcacaGLPaaacqGH9aqpdaWdXbqaaiaabs7aaSqaaiabgkHiTiabg6HiLcqaaiabg6HiLcqdcqGHRiI8aOWaaeWaaeaacaWG0bGaeyOeI0IaamiDamaaBaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiaadAgadaqadaqaaiaadshaaiaawIcacaGLPaaacaqGKbGaamiDaaaa@4CD4@ .

Note 2 to entry: Any shape with area 1 may be used for the definition of δ(t), e.g. a rectangular pulse with width τ and height τ–1, or a triangular pulse, as shown in Figure 4a), as well as a Gaussian function

1 τ π e t 2 τ 2 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaamaalaaabaGaaGymaaqaaiabes8a0jabgwSixpaakaaabaGaeqiWdahaleqaaaaakiabgwSixlaadwgadaahaaWcbeqaaiabgkHiTiaaykW7caaMc8+aaSaaaeaacaWG0bWaaWbaaWqabeaacaaIYaaaaaWcbaacdaGae8hXdq3aaWbaaWqabeaacaaIYaaaaaaaaaaaaa@4823@ .

Note 3 to entry: Any of the shapes mentioned in Note 2 to entry with τ much smaller than the smallest time constant at work in the system under consideration may be used for a technical approximation of the Dirac impulse.

Note 4 to entry: In control technology the Dirac function is mainly important for the definition of impulses and exclusively used as a function of time. Therefore the term Dirac impulse is used and the definition is adapted accordingly.


Publication date:2013-11
Source:
Replaces:
Internal notes:2017-06-02: Cleanup - Remove Attached Image 351-45-201_en.gif
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5: