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DiracComb[x]

represents the Dirac comb function TemplateBox[{{x}}, DiracCombSeq] giving a delta function at every integer point.

DiracComb[x1,x2,…]

represents the multidimensional Dirac comb function TemplateBox[{{{x, _, 1}, ,, {x, _, 2}, ,, ...}}, DiracCombSeq].

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Numerical Evaluation  
Function Properties  
See Also
Related Guides
History
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DiracComb

DiracComb[x]

represents the Dirac comb function TemplateBox[{{x}}, DiracCombSeq] giving a delta function at every integer point.

DiracComb[x1,x2,…]

represents the multidimensional Dirac comb function TemplateBox[{{{x, _, 1}, ,, {x, _, 2}, ,, ...}}, DiracCombSeq].

Details

  • DiracComb is also known as impulse train, sampling function, and shah.
  • DiracComb[x] is equivalent to .
  • DiracComb can be used in derivatives, integrals, integral transforms, and differential equations.
  • DiracComb has attribute Orderless.

Examples

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Basic Examples  (3)

DiracComb vanishes for noninteger arguments:

Wolfram Language code: DiracComb[1 / 2]

DiracComb stays unevaluated for integer x:

Wolfram Language code: {DiracComb[0], DiracComb[10!]}

Plot over a subset of the reals:

Wolfram Language code: Plot[DiracComb[x], {x, -2, 2}, AxesOrigin -> {0, -1}]

The Fourier transform of DiracComb is a DiracComb:

Wolfram Language code: FourierTransform[DiracComb[x], x, ω]

Scope  (8)

Numerical Evaluation  (4)

Evaluate numerically:

Wolfram Language code: DiracComb[1 / 7]
Wolfram Language code: DiracComb[4, 8, 1 / 3]

DiracComb always returns an exact 0:

Wolfram Language code: DiracComb[.1]
Wolfram Language code: DiracComb[.1435345345678990]

Evaluate efficiently at high precision:

Wolfram Language code: DiracComb[1 / 74, 1 / 8, 1 / 3`100]//Timing
Wolfram Language code: DiracComb[1 / 9, 1 / 8, 1 / 3`10000000];//Timing

DiracComb threads over lists:

Wolfram Language code: DiracComb[{-.5, 0, .5}]

Function Properties  (4)

Function domain of DiracComb:

Wolfram Language code: FunctionDomain[DiracComb[x], x]

It is restricted to real arguments:

Wolfram Language code: FunctionDomain[DiracComb[z], z, Complexes]

DiracComb is an even function:

Wolfram Language code: DiracComb[-x]

The multivariate DiracComb is a product of univariate ones:

Wolfram Language code: FunctionExpand[DiracComb[x, y]]

TraditionalForm formatting:

Wolfram Language code: DiracComb[x]//TraditionalForm
Wolfram Research (2008), DiracComb, Wolfram Language function, https://reference.wolfram.com/language/ref/DiracComb.html.

Text

Wolfram Research (2008), DiracComb, Wolfram Language function, https://reference.wolfram.com/language/ref/DiracComb.html.

CMS

Wolfram Language. 2008. "DiracComb." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiracComb.html.

APA

Wolfram Language. (2008). DiracComb. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiracComb.html

BibTeX

@misc{reference.wolfram_2026_diraccomb, author="Wolfram Research", title="{DiracComb}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/DiracComb.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_diraccomb, organization={Wolfram Research}, title={DiracComb}, year={2008}, url={https://reference.wolfram.com/language/ref/DiracComb.html}, note=[Accessed: 13-June-2026]}