@chervokas - to be entirely correct, it is just Fourier Transform (FT). FFT is a Fast Fourier Transform which is an algorithm (one of many) that implements FT in discrete form for a typical computer chip. FFT is only approximation, it is NEVER precise as Fourier sequence is infinite for complex signals like music. Thus, ANY transfer to frequency domain and back (such as for Dirac) is somewhat lossy. Discrete chips and methods all have limited precision.
I’m just noting that our hearing in fact does work in some ways that are analogous to a FT, in that our ears and brains break down an incoming complex wave into it’s component discrete frequencies. Our ears and brains don’t seem to have to flip between frequency and time domains, so that's a substantial difference in kind, we seem to be able to process both simultaneously by processing information from the location on the cochlea that is activated and the timing pattern of the neural firing so activated -- at least up to about 4kHz or 5 kHz above which our neural ability to phase lock to the signal breaks down, our perception of pitch starts to break down, and our ability to resolve timing with respect to frequency becomes less precise and depends on information we can glean from other biological processes.
But like anything else, our ears and brains are definitely far from infinite in resolution, highly non-linear even in the frequencies and spls and time increments that we can resolve, and limited in precision too.