Talk:Convolution

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I originally wrote:

In electrical engineering, the output of a linear system is the convolution of the input with the system's response to an impulse.

Akella changed it to:

In Systems Science, the output of a linear system is the convolution of the input with the system's response to an impulse.

I have a problem with that, because I know of no such discipline as Systems Science, and neither, at this point, does Wikipedia. I know of "system analysis," but as a rather imprecisely defined terms that once may have had an engineering meaning, and then became something like a high-ranking computer programmer...

I realize that the scope is much broader than electrical engineering, but I was trying to list some contexts, that might be familiar to readers, in which convolution makes an appearance.

Also, in electrical engineering, the phrase "linear system" is often used to refer to precisely the kind of system described by a one-dimensional convolution integral. Whereas, in other fields, such as, say, Linear algebra, the scope of the word "linear system" is much broader, so you couldn't just say "linear system" and leave it at that.

So, I've changed it to:

In electrical engineering and other disciplines, the output of a linear system is the convolution of the input with the system's response to an impulse

Dpbsmith 23:58, 26 Feb 2004 (UTC)

It might be worth noting that the university I'm at has a School of Systems Engineering, which includes departments of Electrical Engineering and Cybernetics (as well as Computer Science). Perhaps the term we're after is somewhere amongst that lot. - IMSoP 00:34, 27 Feb 2004 (UTC)

I'm certainly not going to get into an edit war over it. I do think electrical engineering should be listed first, for the very personal POV reason that it's where I first encountered convolutions, and that any other disciplines that are mentioned should be ones that are a) readily recognizable to a reader, and b) ones in which any graduate with a degree in that discipline would instantly recognize the word "convolution" and know what it meant.... Dpbsmith 11:53, 27 Feb 2004 (UTC)

How about "In disciplines such as Electrical Engineering and Cybernetics...", just to be a bit less vague than "and other disciplines"? - IMSoP 18:11, 27 Feb 2004 (UTC)

Your call. Your edit. "Be bold." Since I think it's OK as is, I won't change it myself, but I certainly wouldn't revert it if you change it. In what course did you encountered the convolution integral and with what discipline do you associate it? Dpbsmith 00:44, 28 Feb 2004 (UTC)

Does the $\sqrt{2\pi}$ factor in the convolution theorem apply where Laplace transforms are concerned? I can see where it comes in for Fourier transforms, but not Laplace transforms. --Glengarry 01:34, 15 Jul 2004 (UTC)

Constant factors like this only depend upon the normalization convention used for the transform in question. (There are normalizations of the Fourier transform, for example, where the constant is unity.) —Steven G. Johnson 04:56, Jul 15, 2004 (UTC)

Anybody know where the term "convolution" comes from? It'd be nice to add this bit of historical trivia.

1 Definition
2 Merging from PlanetMath
3 Broken link
4 Risk theory
5 multi-dimensional convolution
6 Convolution kernel
7 Convolution of measures
8 Convolution Matrices needed

[edit] Definition

The definition is not satisfying. What exactly are f and g? Something like $f, g: D \to\Bbb C$ ? --Bfrey 14:58, 10 May 2006 (UTC)

[edit] Merging from PlanetMath

The PlanetMath has a nice GFDL article on convolution, see http://planetmath.org/?op=getobj&from=objects&id=2790 Anybody willing to merge that stuff? Oleg Alexandrov (talk) 02:17, 24 November 2005 (UTC)

[edit] Broken link

Hi - The link to 'Convolution' on Planet Math in the external links section seems to be broken. --anon

Now it works. I guess the PlanetMath websiste was down or something. Oleg Alexandrov (talk) 22:42, 6 January 2006 (UTC)

[edit] Risk theory

in risk theory the distribution of the sum of n i.i.d random variables is found by convolution.

[edit] multi-dimensional convolution

For things like image processing we have 2d convolution $blurry(u,v) = \int\int f(u, v)g(u-\upsilon, v - \nu) d\upsilon d\nu$ . Could someone who knows about this stuff explain how this works, and the rules for separating orders (I think it's the same as the theorem that allows 2d FT to be composed using two 1D FTs?) --njh 05:25, 19 April 2006 (UTC)

[edit] Convolution kernel

Convolution kernel points here. This article should define it. - 72.58.19.66 05:55, 23 May 2006 (UTC)

shouldn't that be rather point to / be defined in integral transform? — MFH:Talk 13:49, 2 June 2006 (UTC)

[edit] Convolution of measures

The notation μ×ν (used in section Convolution of measures) is not explained here, neither in Borel measure or any other (more or less "directly") linked page. I am not used to work on this subject, but from the background I have, I suspect it should rather be denoted as a tensor product $\mu\otimes\nu$ . (The only definitions I know for a "cross product" are the vector cross product and the Cartesian product of sets, but not of maps.) — MFH:Talk 13:49, 2 June 2006 (UTC)

[edit] Convolution Matrices needed

Please add a page listing different image processing convolution kernel matrices since there seems to be no good general reference for them on the web. Include the matrix values as well as a description of what the convolution kernel does.

it might be nice to see a discussion of convergence issues. E.g. the convolution operator F(f):=f*g is a linear operator on L^1 if g is in L^1. What other spaces does that hold for?

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