How is frequency information extracted from a waveform?

Question

Examples: frequency analyzers, spectral view in audio editing software

Answer 1

If the highest frequency in the waveform is relatively low so that an analog to digital sampling can run twice as fast, sample the waveform in time domain then do an FFT to obtain the frequency spectrum.

If the highest frequency is too high to be sampled and digitized directly, run the waveform through a heterodyning mixer, sample and FFT the intermediate frequency, then add the mixer's frequency displacement to the spectrum display.

Answer 2

Transforms