Questions on the (continuous or discrete) convolution of two functions.
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0answers
4 views
Is deconvolution simply division in frequency domain?
Is it correct to say that deconvolution simply division in frequency domain?
And that convolution is multiplication in frequency domain.
And to notate a function in frequency domain with a hat above ...
1
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0answers
38 views
clarification asked for 'difference between convolution and crosscorrelation?'
I don't understand answer formulated in ways like this "Thus, $p\ast q$ is the distribution of $X+Y$.
The cross-correlation $p\circ q$ is the distribution $c=(c_n)_n$ defined by ...
2
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0answers
38 views
Why matrix representation of convolution cannot explain the convolution theorem?
A record saying that Convolution Theorem is trivial since it is identical to the statement that convolution, as Toeplitz operator, has fourier eigenbasis and, therefore, is diagonal in it, has ...
-1
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0answers
13 views
Uniform Convergence of Convolutions
$\displaystyle Q_n(t) = ne^{-nt}$
$Qn(t)*f(x) = \int_0^{\infty} Q_n(t)*f(x-t) dt$
How do I prove that this converges uniformly? It seems to be similar to the proof of the
Weierstrass ...
2
votes
1answer
39 views
convolution-distributions
We denote by $E'(\mathbb{R})$ the set of distribution with compact support , and $\mathcal{D}(\mathbb{R})$ is the set of function $\mathcal{C}^{\infty}$ with a compact support.
1) I want to compute ...
0
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1answer
51 views
Is the convolution an invertible operation?
If I have a signal $f(x,y)$ (discrete) and I convolve this signal with a kernal $h(x,y)$:
$y(x,y) = f(x,y) \star h(x,y)$ (where $\star$ is the convolution operator)
Can I obtain $f(x,y)$ given only ...
0
votes
1answer
17 views
Integration function spherical coordinates, convolution
How can I calculate the following integral explicitly:
$$\int_{R^3}\frac{f(x)}{|x-y|}dx$$
where $f$ is a function with spherical symmetry that is $f(x)=f(|x|)$?
I tried to use polar coordinates at ...
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0answers
30 views
Discrete convolution: where do I go from there?
I took this from the book Signals and Systems by Haykin.
I have the following discrete system: $y[n] = u[n]*u[n-3]$, where $*$ is the discrete convolution and $u[n]$ is the unit step function, and ...
0
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0answers
30 views
Strange convolution equation
In an article ( https://www.dropbox.com/s/3012v4s1ngpimvg/gridding_Schomberg_Trimmer.pdf ) about implementation of Gridding method for parallel-beam tomography there's an equation(#47 in the article):
...
1
vote
2answers
39 views
convolution computation involving $e^{-x^2}$
In working a problem involving convolution, I have arrived at the following integral, but do not know how to compute it:
$$2\int_0^{\infty}e^{-a(x-y)^2-by^2}dy$$
I thought that this integrand did not ...
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1answer
27 views
Function as a convolution product of other two
I need help with this:
I have to prove that a function $f\in L_{2}(T)$ can be expressed as $f=g*h$ (convolution product) for some functions $g,h\in L_{2}(T)$ if and only if $(\hat{f}(n))_{n}\in ...
0
votes
1answer
35 views
Differentiability of convolution
First let me say that I have used the search bar and looked through all the "differentiability of convolution" questions that I saw, but none of them seem to cover this case. (If one of them did and I ...
3
votes
0answers
69 views
Infinite self-convolution for a function
I have a mathematical problem that leads me to a particular necessity. I need to calculate the convolution of a function for itself for a certain amount of times.
So consider a generic function $f : ...
0
votes
1answer
27 views
Need help with convolution problem.
I'm just learning about the convolution integral and am stuck on this example problem:
Given
$x_1(t) = \left \{\begin{array}{lr} 1 : 0 < x < 1 \\ 0: \text{elsewhere} \end{array} ...
1
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0answers
36 views
Fubini theorum for integrating 1 dimension of a 3d convolution
I have 3D volume that is convoluted with a 3D blur function. Both are positive and integrate to a finite value. I can see experimentally (meaning playing with matlab) that this is true:
$\int_{-a}^{a ...
