This question came up while I was studying matched filters and their cross-correlating behavior at the output.
Given that autocorrelation is just a specific type of cross-correlation. When cross-correlating a function $f(x)$ with its time inversed and complex conjugate $f^*(-x)$ as is the behavior of the matched filter on the output, does this simplify down to the auto-correlation of $f(x)$?
I am currently studying "Upamanyu Madhow - Introduction to Communication Systems-Cambridge University Press (2014)" but since this question is more mathematical in nature, any suggested literature on the concept will be welcomed.
Autocorrelation is the cross-correlation of a time series with itself.
As noted here, the cross-correlation of $f(t)$ and $g(t)$ is equivalent to the convolution of $f(t)$ and $g^*(-t)$. Applying this to your case, the autocorrelation of $f(t)$ is equivalent to the convolution of $f(t)$ with $f^*(-t)$ (not the autocorrelation of the two).