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Suppose $f(x)$ and $g(x)$ are two functions. What is intuition or idea behind the convolution of $f$ and $g$? After taking the convolution we will get a new function. What is the geometric relation between $f$, $g$, and $f*g$ ?

Joseph Quinsey
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Kumar
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    Have a look at this: http://www.jhu.edu/signals/convolve/ – Giuseppe Negro Jan 23 '13 at 05:26
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    See also http://upload.wikimedia.org/wikipedia/commons/6/6a/Convolution_of_box_signal_with_itself2.gif – Thomas Jan 23 '13 at 06:49
  • The images at http://en.wikipedia.org/wiki/Convolution are very useful, as pointed out by @macydanim. Since convolution is linear in each function, you can try to get a feeling for the general situation by considering step functions using linear combinations of the first animation. – user108903 Jan 23 '13 at 07:45

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I suspect this can be answered by a google search or a wikipedia search on the site. Usually people think $f*g$ as an "average" of $f$ with $g$, such that $f*g$ has at least as nice properties as $f$ and $g$. I am sure other people at here can give a much better answer, but hopefully the meaning of it will be clear if you encounter Fourier series or Fourier transform, since that's where they appear most naturally and frequently.

Bombyx mori
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