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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 Examplesopen allclose all 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. TextWolfram Research (2008), DiscreteConvolve, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteConvolve.html.
CMSWolfram Language. 2008. "DiscreteConvolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteConvolve.html.
APAWolfram 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: 12-July-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: 12-July-2025 ]}
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