Saturation is represented by repeating harmonics through a spectrogram. Both hardware and software spectrograms are available for you to try out: you'll very quickly figure out the patterns it produces if you watch carefully.
It may be a bit of an overkill for audio, since I am not quite sure how consistently these systems usually perform across their entire bandwidth.
[1] https://en.wikipedia.org/wiki/Third-order_intercept_point#De...