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.
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
- The convolution of two sequences and is given by .
- The multidimensional convolution is given by .
- The following options can be given:
-
Examples
open all close allBasic 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)
DiscreteConvolve computes a sum over the set of integers:
Convolution with DiscreteDelta gives the value of a sequence at m:
Scaling:
Commutativity:
Distributivity:
The ZTransform of a causal convolution is the product of the individual transforms:
Similarly for GeneratingFunction :
The FourierSequenceTransform of a convolution is the product of the individual transforms:
Interactive Examples (1)
This demonstrates the discrete-time convolution operation :
Related Guides
Related Links
History
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: 17-November-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: 17-November-2025]}