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Convolve[f,g,x,y]
gives the convolution with respect to x of the expressions f and g.
Convolve[f,g,{x1,x2,…},{y1,y2,…}]
gives the multidimensional convolution.
Details and Options Examplesopen allclose all Basic Examples (3)Convolve a function with DiracDelta:
Convolve two exponential functions and plot the result:
Scope (5) Univariate Convolution (3)The convolution gives the product integral of translates:
A convolution typically smooths the function:
For this family, they all have unit area:
Multivariate Convolution (2)The convolution gives the product integral of translates:
Convolution with multivariate delta functions acts as a point operator:
Convolution with a function of bounded support acts as a filter:
Generalizations & Extensions (1)Multiplication by UnitStep effectively gives the convolution on a finite interval:
Options (2) Assumptions (1)Specify assumptions on a variable or parameter:
GenerateConditions (1)Generate conditions for the range of a parameter:
Properties & Relations (7)Convolve computes an integral over the real line:
Convolution with DiracDelta gives the function itself:
The Laplace transform of a causal convolution is a product of the individual transforms:
The Fourier transform of a convolution is related to the product of the individual transforms:
Interactive Examples (1)This demonstrates the convolution operation :
Wolfram Research (2008), Convolve, Wolfram Language function, https://reference.wolfram.com/language/ref/Convolve.html. TextWolfram Research (2008), Convolve, Wolfram Language function, https://reference.wolfram.com/language/ref/Convolve.html.
CMSWolfram Language. 2008. "Convolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Convolve.html.
APAWolfram Language. (2008). Convolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Convolve.html
BibTeX@misc{reference.wolfram_2025_convolve, author="Wolfram Research", title="{Convolve}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Convolve.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_convolve, organization={Wolfram Research}, title={Convolve}, year={2008}, url={https://reference.wolfram.com/language/ref/Convolve.html}, note=[Accessed: 12-July-2025 ]}
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