This is the kind of explanation I was looking to post on here, but couldn't quite formulate it right in my head. Yours is very clear. Interestingly, it was ac

This is the kind of explanation I was looking to post on here, but couldn't quite formulate it right in my head. Yours is very clear. Interestingly, it was actually learning quantum mechanics that made me understand the Fourier Transforms much more easily. You're always projecting the wavefunction into some basis, so the cosines and sines are just one particular basis.