I once read an explanation of the Fourier transformation as akin to looking at a fully blended smoothie and being able to calculate exactly how much of each ingredient went into it.

I don't profess to be a DSP expert whatsoever, but the more familiar I've become with Fourier transformations, the more apt that analogy seems. Once you grasp that all sound is just a large addition problem of many, many sine waves, the ability to distinguish between them to a fairly high degree of fidelity feels almost like magic.