I have a background in physics, and I've done a graduate class in harmonic analysis (although this was very theoretical class in a Hilbert space setting), plus I recently started DJing as a hobby. I've very recently began tying learn about about processing sound signals to hopefully get more creative at my craft. What I'm about to ask here is very non-rigorous though.
What I wanted to ask is, (assuming a high sample rate obviously for the original recording) how does a digital sound signal for some song allow us to actually distinguish each individual instrument? Eg, if we play rock song, we can clearly distinguish the drums, bass guitar, lead guitar and vocals by ear. They each have a distinguishable sound. What specifically in the digital audio signal allows us to recognize this by ear?
I can understand that a Fourier transform may be a good way to distinguish the sound of each different instrument mathematically, perhaps it has something to do with that? I don't know.