DiscreteConvolve

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

DiscreteConvolve[f,g,{n₁,n₂,…},{m₁,m₂,…}]

gives the multidimensional convolution.

Details and Options

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

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Convolve a sequence with DiscreteDelta:

Convolve two exponential sequences:

Convolve two UnitBox sequences and plot the result:

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:

Specify assumptions on a variable or parameter:

Generate conditions for the range of a parameter:

Obtain a particular solution for a linear difference equation:

Obtain the step response of a linear, time-invariant system given its impulse response h:

The step response corresponding to this system:

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:

The FourierSequenceTransform of a convolution is the product of the individual transforms:

This demonstrates the discrete-time convolution operation :

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