This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# DiscreteConvolve

 DiscreteConvolve gives the convolution with respect to n of the expressions f and g. DiscreteConvolvegives the multidimensional convolution.
• 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
Convolve two sequences:
Use a typical impulse response h for a system:
The step response corresponding to the same system:
Convolve two sequences:
 Out[1]=
 Out[2]=

Use a typical impulse response h for a system:
 Out[2]=
The step response corresponding to the same system:
 Out[3]=
 Out[4]=
 Scope   (4)
Convolution sums the product of translates:
Convolution of elementary sequences:
Convolution of piecewise sequences:
Multiplication by UnitStep effectively gives the convolution over a finite interval:
 Options   (2)
Specify assumptions on a variable or parameter:
Generate conditions for the range of a parameter:
 Applications   (1)
Obtain a particular solution for a linear difference equation:
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:
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