Can you expand a little further? I don't see the adjunction (between what categories?)

It's somewhat weird to see someone immediately jump to category theory when it's more likely to be about basic linear algebra.

That said convolution and correlation are not linear operators but bilinear operators, so I'm struggling a bit to see in what sense they're adjoint.

Maybe something like:

<Conv(x,y), z> = <y, Corr(x, z)>

which does actually work if you let the inner product be the integral of the product and the correlation the time-correlation (so the inner product is the correlation at time 0).

That is what I was referring to yes, however it is also adjoints in the category theory sense.

http://www.reproducibility.org/RSF/book/bei/conj/paper_html/...

Ah I see; The word "adjoint" tripped me up, I presumed they meant "adjunction", and not the matrix-transpose-adjoint :)

i GUESS what he means is something like inverse of covariance matrix gives correlation matrix, something like this question: https://stats.stackexchange.com/q/140080