# Can Mathematica reconstruct an audio signal from a given spectrogram

I just realized that Mathematica can easily construct a spectrogram for a given .wav file. My question is, to what extent can this process be inverted in Mathematica?

Namely, lets say I have the data generated from the SpectrogramArray function and somehow I've lost the original .wav file or I have applied some kind of effects to the data. Now is there a way to "play back" the spectrogram? Admittedly, this question is vague because as I understand phase information is lost in passing from audio signal to spectrogram, however a good amount of literature exists on reconstructing signals from the absolute short-time Fourier transform and I was wondering if any of these have been implemented in Mathematica or if there is some straightforward way to do so.

Many thanks!

• InverseFourier is the inverse of Fourier; try getting your spectogram data into the same format. Phase differences typically are not audible. – CL. Nov 26 '14 at 11:34