Ever wondered how you can play a chord on the piano where each key produces a different frequency, but you only see one waveform when you record it into your daw?
In more technical words, how can a chord at a given time be represented by a single bit value?

Thank Joseph Fourier!

The Fourier equations take frequency information and converts it into the time domain, and vice versa. Sound familiar? Kinda like your AD and DA? Correct!
The AD performs the Inverse Fourier transform to convert frequency information into time that can be captured by a bit.
The DA performs the regular (or Forward) Fourier transform to convert those bits back into frequency information.

For more info checkout the Gizmodo article:

For the actual math, checkout this video

 

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This video

 

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Simple answer: It can't.

Not at all!
An ADC samples an analog signal periodically and for each sample interval, it measures its value and converts it to a digital word.
A DAC converts a digital word to an analog voltage, also usually at periodic time intervals (44100 conversions per second is a common value).

You can only perform a Fourier transform on a set of numerical sample values, i.e. after, Analog-to-digital conversion.
It's a completely separate process that has nothing to do with ADC or DAC.