Is it easy to recreate audio from, say, an image file of the spectrogram results?
Click waterfall, and then click play when you have the audio on your computer playing outloud.
If you play the audio outloud, your mic should be able to pick up a barely recognizable version of the picture (try the heart first to calibrate the "row delay").
https://github.com/braeden/waterfall
Take a look at the example pictures on github ^, poor, but functional fully web version.
The spectrogram image contains amplitude, but not phase information. (There are partial exceptions in special cases involving oversampling.) Conveniently, the human auditory system is primarily sensitive to the same information present in the spectrogram.
I have been told audio -> FFT —> audio (the kind of standard audio compression/decompression algorithms we use) lose that phase information and we can't tell.
I have been told the "phase information" is the imaginary part of the complex numbers that are involved in an FFT.
Demonstration of this being done: http://arss.sourceforge.net/examples.shtml