Convolution Intuition Sliding

Question

I understand it as follows please correct me if I am wrong.

There are two functions $f(x)$ and $g(x)$. I am sliding $g(x)$ over $f(x)$, we find area for a given interval "$t$" which is the area where both $f(x)$ and $g(x)$ intersects(shown as yellow area) and we plot the same area value as a black line which is the convolution function. So does convolution function gives this equation form? So the equation form gives the value of the area for different $f(x)$ and $g(x)$ values.

I'm not sure what your question is. But you may find this MO link helpful: http://mathoverflow.net/questions/5892/what-is-convolution-intuitively — Gyu Eun Lee, Nov 16 '16 at 08:49

score 1 · Answer 1 · answered Nov 16 '16 at 10:10

Explanation of wikipedia's explanation.

They first flip one of the functions, $g_-(x) = g(-x)$. So that $f(\tau)g(t-\tau)$ becomes $f(\tau)g_-(\tau-t)$.

Suppose you want to find the value of the convolution at, say $t=1.7$. Let $g^{1.7}_- = g_-(\tau-1.7)$ be the function $g_-$ shifted left.

Now, the integral of $f(\tau) g^{1.7}_-(\tau)$ should be a familiar object, which, in some cases (when one of the function has values $\{0, 1\}$), can be interpreted as the area of intersection of the two functions, both of which should be easy to visualize.

Convolution Intuition Sliding

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