gives the discrete delta function , equal to 1 if all the ni are zero, and 0 otherwise.



open allclose all

Basic Examples  (3)

Evaluate numerically:

Use in sums:

Plot over a subset of the integers:

Scope  (24)

Numerical Evaluation  (4)

Evaluate numerically:

Complex number inputs:

DiscreteDelta always returns an exact result irrespective of the precision of the input:

Evaluate efficiently at high precision:

Specific Values  (4)

Value at zero:

Multiargument form gives 1 when all inputs are zero:

Value at infinity:

Evaluate symbolically:

Visualization  (3)

Plot the single-argument DiscreteDelta using integer-width bins:

Visualize DiscreteDelta over the reals. Except for a jump at , it is indistinguishable from a zero function:

Plot DiscreteDelta in three dimensions:

Function Properties  (9)

DiscreteDelta is defined for all real and complex inputs:

Function range of DiscreteDelta:

The function range for complex values is the same:

DiscreteDelta is not an analytic function:

Has both singularities and discontinuities:

DiscreteDelta is neither nondecreasing nor nonincreasing:

DiscreteDelta is not injective:

DiscreteDelta is not surjective:

DiscreteDelta is non-negative:

DiscreteDelta is neither convex nor concave:

TraditionalForm typesetting:

Differentiation and Integration  (4)

First derivative with respect to x:

Series expansion at a generic point:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

More integrals:

Applications  (4)

Use in sums to pick out terms:

Pick out elements:

Patch pointwise values of piecewisedefined functions:

Define some finite duration signals:

Plot the signals in the time domain:

To find the convolution of these signals, first calculate the product of the transforms:

Then, perform inversion back to the time domain:

Plot the convolution in the time domain:

Alternatively, find the convolution using DiscreteConvolve:

Properties & Relations  (3)

Reduce an equation containing DiscreteDelta:

The support of DiscreteDelta has measure zero:

DiscreteDelta can be represented as a DifferenceRoot:

Possible Issues  (2)

DiscreteDelta can stay unevaluated with numeric arguments:

A larger setting for $MaxExtraPrecision can be needed:

Equality testing of the arguments takes numerical precision into account:

Wolfram Research (1999), DiscreteDelta, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteDelta.html.


Wolfram Research (1999), DiscreteDelta, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteDelta.html.


Wolfram Language. 1999. "DiscreteDelta." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteDelta.html.


Wolfram Language. (1999). DiscreteDelta. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteDelta.html


@misc{reference.wolfram_2024_discretedelta, author="Wolfram Research", title="{DiscreteDelta}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/DiscreteDelta.html}", note=[Accessed: 18-July-2024 ]}


@online{reference.wolfram_2024_discretedelta, organization={Wolfram Research}, title={DiscreteDelta}, year={1999}, url={https://reference.wolfram.com/language/ref/DiscreteDelta.html}, note=[Accessed: 18-July-2024 ]}