DiscreteDelta
DiscreteDelta[n1,n2,…]
gives the discrete delta function , equal to 1 if all the ni are zero, and 0 otherwise.
Details

- DiscreteDelta[0] gives 1; DiscreteDelta[n] gives 0 for other numeric n.
- DiscreteDelta has attribute Orderless.
Examples
open allclose allScope (24)
Numerical Evaluation (4)
DiscreteDelta always returns an exact result irrespective of the precision of the input:
Specific Values (4)
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:
Applications (4)
Use in sums to pick out terms:
Patch pointwise values of piecewise‐defined 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:
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