gives the convolution with respect to x of the expressions f and g.
gives the multidimensional convolution.
Details and Options
- The convolution of two functions and is given by .
- The multidimensional convolution is given by .
- The following options can be given:
Assumptions $Assumptions assumptions to make about parameters GenerateConditions False whether to generate conditions on parameters Method Automatic method to use PrincipalValue False whether to use principal value integrals
Examplesopen allclose all
Basic Examples (3)
Convolve a function with DiracDelta:
Univariate Convolution (3)
Generalizations & Extensions (1)
Multiplication by UnitStep effectively gives the convolution on a finite interval:
Obtain a particular solution for a linear ordinary differential equation using convolution:
Obtain the step response of a linear, time-invariant system given its impulse response h:
The step response of the system:
Convolving the PDF of UniformDistribution with itself gives a TriangularDistribution:
UniformSumDistribution[n] is the convolution of n UniformDistribution PDFs:
ErlangDistribution[k,λ] is the convolution of k ExponentialDistribution[λ] PDFs:
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:
Wolfram Research (2008), Convolve, Wolfram Language function, https://reference.wolfram.com/language/ref/Convolve.html.
Wolfram Language. 2008. "Convolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Convolve.html.
Wolfram Language. (2008). Convolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Convolve.html