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What does overlap mean in the case of two functions. Or atleast, what does overlap mean in the case of 2 lines or 2 curves.

Thanks in advance.

The complete sentence to clarify the context:

Convolution is a mathematical operation that takes two functions and measures their overlap. To be more specific, it measures the amount of overlap as you slide one function over another. For example, if two functions have zero overlap, the value of their convolution will be equal to zero. If they overlap completely, their convolution will be equal to one. As we slide between these two extreme cases, the convolution will take on values between zero and one.

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It can mean different things depending on the precise context. Could you please post (i) the complete sentence that contains the word; and (ii) the source of that sentence? –  Arturo Magidin Feb 23 '12 at 17:46
    
I edited the questions. Thanks for the response. –  user907629 Feb 23 '12 at 18:40
    
Did you try this? –  draks ... Feb 23 '12 at 19:17
    
That link is not much help because I am trying to understand what does overlap mean in this context. –  user907629 Feb 23 '12 at 19:20

1 Answer 1

up vote 2 down vote accepted

The animated picture in the link draks gave you gives you the basic idea. If you pause the animation at any given point, the "overlap" refers to the area in yellow.

If you imagine a function as corresponding to its graph on the plane, you can take two functions, $f$ and $g$, graph them on separate transparent sheets of plastic, and then place the two sheets one on top of the other; "overlap" would refer to the section of the plane that lies simultaneously between the $X$-axis and the graph of $f$, and between the $X$-axis and the graph of $g$.

The problem with this simple minded comparison is that you can have two identical functions, but one of them "shifted horizontally" so that there is no overlap between the two graphs. The convolution accounts for this by "sliding" one of the two graphs horizontally and measuring the overlap then, and "adding it up".

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Thanks for the help. I am unable to vote up your comment because, i dont have enough reputation. –  user907629 Feb 24 '12 at 4:52

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