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DiscreteConvolve

DiscreteConvolve
gives the convolution with respect to n of the expressions f and g.
DiscreteConvolve
gives 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$Assumptionsassumptions to make about parameters
GenerateConditionsFalsewhether to generate conditions on parameters
MethodAutomaticmethod to use
VerifyConvergenceTruewhether 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:
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Use a typical impulse response h for a system:
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The step response corresponding to the same system:
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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:
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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