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I am currently learning about the concept of convolution between two functions in my university course. The course notes are vague about what convolution is, so I was wondering if anyone could give me a good explanation. I can't seem to grasp other than the fact that it is just a particular integral of two functions. What is the physical meaning of convolution and why is it useful? Thanks a lot.

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Here's a nice thread on MathOverflow about this: – Rahul Oct 21 '10 at 15:00
up vote 5 down vote accepted

Have a look here:

...and lots of good answers here:

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Thanks for the links. From the two, I found the second link to be better for understanding. Now I have some sort of "intuition" for convolutions! =) – thomas1234 Oct 21 '10 at 15:18

I'd suggest these lectures by professor Osgood here

particularly lectures 8 and 9.

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this link has expired... I think this is the current location: – user2740 Nov 19 '15 at 11:10

The Wikipedia has some nice graphical explanations.

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Although I've already read the wikipedia entry, thanks for your input =) – thomas1234 Oct 21 '10 at 15:20

If $X$ and $Y$ are random variables, then their sum $X+Y$ is the convolution of their distributions.

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The way you have stated this is a bit unclear. the distribution of the variable $Z = X + Y$ is the convolution of the distributions of $X$ and $Y$. This is true only when $X$ and $Y$ are independent. – svenkatr Oct 25 '10 at 19:20

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