gives the convolution with respect to n of the expressions f and g.
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:
Assumptions $Assumptions assumptions to make about parameters GenerateConditions False whether to generate conditions on parameters Method Automatic method to use VerifyConvergence True whether to verify convergence
Examplesopen allclose all
Basic Examples (3)
Generalizations & Extensions (1)
Multiplication by UnitStep effectively gives the convolution over a finite interval:
Properties & Relations (7)
DiscreteConvolve computes a sum over the set of integers:
Convolution with DiscreteDelta gives the value of a sequence at m:
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: