BUILT-IN MATHEMATICA SYMBOL

DiscreteConvolve

gives the convolution with respect to n of the expressions f and g.

DiscreteConvolve

gives the multidimensional convolution.

MORE INFORMATION

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

EXAMPLES

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Basic Examples (2)

Convolve two sequences:

Use a typical impulse response h for a system:

The step response corresponding to the same system:

Convolve two sequences:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Use a typical impulse response h for a system:

In[1]:=

In[2]:=

Out[2]=

The step response corresponding to the same system:

In[3]:=

Out[3]=

In[4]:=

Out[4]=

Scope (4)

Convolution sums the product of translates:

Convolution of elementary sequences:

Convolution of piecewise sequences:

Generalizations & Extensions (1)

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:

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: