The problem (taken from here) asks for possible sampling rates that will not cause aliasing in the following frequency spectrum:
The range of possible values after some math is given as $B_2 < f_s < 2B_1$. As an example, they provide the following image:
I understand the frequency spectra do not overlap, which is why we have the solution given in the key. However, I'm curious as to why frequencies not overlapping means that no aliasing occurs. The periodized version of the spectra (at the lower sampling rate) looks nothing like the original spectra, which I believe should cause a different signal than the original one to be computed. How would signal reconstruction know to avoid the 'doubling' this apparent mirroring and doubling?