DiscreteConvolve—Wolfram Language Documentation (original) (raw)

BUILT-IN SYMBOL

• See Also
  • Sum
  • Convolve
  • ListConvolve
  • ZTransform
  • GeneratingFunction
  • FourierSequenceTransform
  • DirichletConvolve
• Related Guides
  • Summation Transforms
  • Fourier Analysis
  • Additive Number Theory

DiscreteConvolve

DiscreteConvolve[f,g,n,m]

gives the convolution with respect to n of the expressions f and g.

DiscreteConvolve[f,g,{n1,n2,…},{m1,m2,…}]

gives the multidimensional convolution.

Details and Options

Examples

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Basic Examples (3)

Convolve a sequence with DiscreteDelta:

Convolve two exponential sequences:

Convolve two UnitBox sequences and plot the result:

Scope (4)

Univariate Convolution (3)

Convolution sums the product of translates:

Convolution of elementary sequences:

Convolution of piecewise sequences:

Multivariate Convolution (1)

Generalizations & Extensions (1)

Multiplication by UnitStep effectively gives the convolution over a finite interval:

Options (2)

Assumptions (1)

Specify assumptions on a variable or parameter:

GenerateConditions (1)

Generate conditions for the range of a parameter:

Applications (2)

Obtain a particular solution for a linear difference equation:

Obtain the step response of a linear, time-invariant system given its impulse response h:

The step response corresponding to this system:

Properties & Relations (7)

Interactive Examples (1)

This demonstrates the discrete-time convolution operation :

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_discreteconvolve, author="Wolfram Research", title="{DiscreteConvolve}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/DiscreteConvolve.html}", note=[Accessed: 14-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_discreteconvolve, organization={Wolfram Research}, title={DiscreteConvolve}, year={2008}, url={https://reference.wolfram.com/language/ref/DiscreteConvolve.html}, note=[Accessed: 14-June-2025 ]}