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Convolve

Convolve
gives the convolution with respect to x of the expressions f and g.
Convolve
gives the multidimensional convolution.
  • The convolution of two functions and is given by .
  • The multidimensional convolution is given by .
  • The following options can be given:
Assumptions$Assumptionsassumptions to make about parameters
GenerateConditionsFalsewhether to generate conditions on parameters
MethodAutomaticmethod to use
PrincipalValueFalsewhether to use principal value integrals
Convolve two functions:
A typical impulse response h for a system:
The step response corresponding to the same system:
Convolve two functions:
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A typical impulse response h for a system:
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The step response corresponding to the same system:
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The convolution gives the product integral of translates:
Elementary functions:
A convolution typically smooths the function:
For this family they all have unit area:
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:
Multiplication by UnitStep effectively gives the convolution on a finite interval:
Specify assumptions on a variable or parameter:
Generate conditions for the range of a parameter:
Obtain a particular solution for a linear ordinary differential equation using convolution:
The convolution of UnitBox with itself is UnitTriangle:
Convolving the PDF of UniformDistribution with itself gives a TriangularDistribution:
UniformSumDistribution[n] is the convolution of n UniformDistribution PDFs:
ErlangDistribution is the convolution of k ExponentialDistribution[] PDFs:
Convolve computes an integral over the real line:
Convolution with DiracDelta gives the function itself:
Scaling:
Commutativity:
Distributivity:
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:
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