UnilateralDiscreteConvolve
UnilateralDiscreteConvolve[f,g,k,n]
gives the unilateral discrete convolution with respect to k of the expressions f and g.
UnilateralDiscreteConvolve[f,g,{k1,…,kp},{n1,…,np}]
gives the multidimensional unilateral discrete convolution.
Details and Options
- UnilateralDiscreteConvolve is also known as causal convolution.
- Unilateral convolution arises naturally when examining causal systems. The output of such systems at any time depends only on values of the input at the present time and in the past.
- The unilateral 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
Examples
open allclose allBasic Examples (4)
Convolve a sequence with DiscreteDelta:
Convolve a pair of step sequences:
Convolve a linear sequence and a harmonic sequence and plot the result:
Scope (6)
Convolve sequences of binomial coefficients:
Convolution of polynomial sequences:
Convolution of exponential sequences:
Convolution of trigonometric sequences:
Multivariate convolution with DiscreteDelta:
Applications (2)
Obtain a particular solution for a linear ordinary difference equation using convolution:
Find the product of two power series:
Verify the result using Sum:
Properties & Relations (8)
UnilateralDiscreteConvolve computes a sum over a finite interval:
Convolution with DiscreteDelta gives the function itself:
DiscreteConvolve coincides with UnilateralDiscreteConvolve for causal sequences:
The Z transform of a causal convolution is a product of the individual transforms:
Verify the convolution theorem for Z transforms on the following example:
The generating function of a causal convolution is a product of the individual generating functions:
Verify the convolution theorem for generating functions on the following example:
Text
Wolfram Research (2024), UnilateralDiscreteConvolve, Wolfram Language function, https://reference.wolfram.com/language/ref/UnilateralDiscreteConvolve.html.
CMS
Wolfram Language. 2024. "UnilateralDiscreteConvolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UnilateralDiscreteConvolve.html.
APA
Wolfram Language. (2024). UnilateralDiscreteConvolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UnilateralDiscreteConvolve.html