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Results tagged with convolution
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user 12679
Tags for questions about convolution, including the Mathematica functions Convolve, DiscreteConvolve, ListConvolve, DirichletConvolve, ImageConvolve, and convolutions using Fourier, FourierTransform, or LaplaceTransform.
3
votes
The curious case of Convolve function
It's my understanding that the convolution operation is supposed to be both commutative and associative. … Evaluate[Convolve[Evaluate[Convolve[v[x, dispersion], u[x, delay, dispersion],
x, y, Assumptions -> x >= 0]], s[f, y, delay, dispersion], y, t, Assumptions -> y >= 0]]];
If we then compute the convolution …
- 455
2
votes
Accepted
Is there an option for InverseLaplaceTransform to make Mathematica use the convolution theor...
I modified @xzczd's code and came up with the following wrapper for the inverse Laplace transform:
ilpt[(h : List | Plus | Equal)[a__], s_, t_] := ilpt[#, s, t] & /@ h[a]
ilpt[a_ b_, s_, t_] :=
Modu …
- 455
1
vote
1
answer
76
views
Is there an option for InverseLaplaceTransform to make Mathematica use the convolution theor...
By default, it appears that Mathematica won't use the convolution theorem to write an inverse Laplace transform in the form of a convolution of two functions. … So, InverseLaplaceTransform[1/(s+1)*LaplaceTransform[f[t],t,s],s,t] should be able to be written as the convolution of e^-t and f[t]. But, Mathematica doesn't do that automatically. …
- 455