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.
Best Answer
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".