Given that we have a frequency response $H(f)$,
What would the inverse fourier transform of
$$|H(f)|^2$$
be in terms of a convolution?
I think it would be simply, $$h(t)*h(t)$$
But the answer seems to be $$h(t)*h(-t)$$
Am I missing something? Is it the absolute value that makes the convolution different?
Note that in general, i.e., for $h(t)\in\mathbb{C}$, the inverse Fourier transform of $|H(f)|^2$ is given by
$$\mathcal{F}^{-1}\big\{|H(f)|^2\big\}=h(t)\star h^*(-t)\tag{1}$$
where $\star$ denotes convolution, because
$$\mathcal{F}^{-1}\big\{H^*(f)\big\}=h^*(-t)\tag{2}$$
and obviously, as pointed out in a comment, we have
$$|H(f)|^2=H(f)\cdot H^*(f)\tag{3}$$