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:

DiracComb stays unevaluated for integer x:

Plot over a subset of the reals:

The Fourier transform of DiracComb is a DiracComb:

Scope  (8)

Numerical Evaluation  (4)

Evaluate numerically:

DiracComb always returns an exact 0:

Evaluate efficiently at high precision:

DiracComb threads over lists:

Function Properties  (4)

Function domain of DiracComb:

It is restricted to real arguments:

DiracComb is an even function:

The multivariate DiracComb is a product of univariate ones:

TraditionalForm formatting:

Introduced in 2008
 (7.0)