Talk:Circular convolution

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Cyclic convolution is already mentioned in convolution, and it's not clear that it needs its own article. In any case, it is logically independent of the DFT — which just happens to give a way to compute cyclic convolutions. Cyclic convolutions are a perfectly well defined mathematical operation, and are often useful in their own right; this article gives the impression that they are always a mere artifact, an unwanted side-effect of a particular FFT-based algorithm.

Moreover, cyclic boundary conditions are merely one possible boundary condition for convolution. One can also have e.g. even/odd boundary conditions of various types. (For example, every type of discrete cosine transform and discrete sine transform corresponds to convolutions with a different distinct boundary condition.)

—Steven G. Johnson 22:05, 9 December 2005 (UTC)

It is even more than "mentioned" in Discrete_Fourier_transform#Circular_convolution_theorem_and_cross-correlation_theorem. And neither article makes all the points made here. So what also is not clear is where these points should be made. There seemed to be a need for its own place to be.

You make some good points about the incompleteness of this article, but merging it into convolution will not address those issues. Instead, why not expand this article? That is actually what I was hoping for when I started it. I know there is a way to indicate that the article is a work in progress. Why not do that?

--Bob K 23:30, 9 December 2005 (UTC)

"Merge" means "add any missing stuff to the other article" not just "delete this article". Why not expand convolution? The various boundary conditions have so much in common, in how you define, understand, and apply them, that it makes more sense to me to describe them all in one place rather than having a separate article for each. —Steven G. Johnson 04:34, 10 December 2005 (UTC)

I understand, because that is what I would have done, except for the Discrete_Fourier_transform#Circular_convolution_theorem_and_cross-correlation_theorem article, which already has a better treatment than convolution. I am not opposed to merging all this stuff, but to be honest, it was much easier to use the powerful advantage of internal links that wikipedia offers. I confess to taking the easy way out of the dilemma. And I don't know as much about convolution as you apparently do, so I am not really in a position to write the definitive article anyway. This article was only meant to plug a small hole that seemed to be overlooked... a simple, graphic, layman's explanation. Demystification, because there is a lot of unnecessary misunderstanding about this relatively simple thing. If it serves as a catalyst for bigger and better things, that's fine too. But I am now satisfied. So that is a project for someone else. --Bob K 18:23, 11 December 2005 (UTC)