DiracComb

DiracComb[x]

represents the Dirac comb function giving a delta function at every integer point.

DiracComb[x1,x2,]

represents the multidimensional Dirac comb function.

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

Basic Examples  (2)

DiracComb vanishes for noninteger arguments:

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DiracComb stays unevaluated for integer x:

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The Fourier transform of DiracComb is a DiracComb:

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See Also

DiracDelta  HeavisideTheta  HeavisidePi  HeavisideLambda  FourierTransform  Convolve  SquareWave

Introduced in 2008
(7.0)