The title and content don't match. The way we distinguish between musical instruments and notes is because of timbre/tone color. Which has nothing to do with f

The title and content don't match. The way we distinguish between musical instruments and notes is because of timbre/tone color. Which has nothing to do with fourier transforms per se and you can use wavelet for that matter. DFT/DTFT are the most common approaches to quantize and convert back to analog and they can be completely left out of the discussion for such a title.