Does an equivalent transformation of a signal to a spectrogram image exist in which the phase information is part of the resulting image?

Question

I'm working on a research project where we would like to apply convolutional neural networks to an image representation of a signal. However, it seems that if I would use a spectrogram, I would end up loosing the phase information. As a result, my question is:

Does an equivalent transformation of a signal to a spectrogram image exist in which the phase information is part of the resulting image?

Thanks a lot and have a great day, Maxime

From https://en.wikipedia.org/wiki/Spectrogram:

Limitations and resynthesis

From the formula above, it appears that a spectrogram contains no information about the exact, or even approximate, phase of the signal that it represents. For this reason, it is not possible to reverse the process and generate a copy of the original signal from a spectrogram.

Answer 1

A homemade solution comes to my mind, but I don't know if it will work for you. I'll write it down anyway, since it may be helpful.

In MATLAB you can do:

[s,f,t] = spectrogram(x,window,noverlap,f,fs);

Thus in s complex values will be stored. You can then find their magnitudes and angles

A = abs(s);
phi = angle(s);

Then you can do a homemade spectrogram with imagesc. For amplitude:

imagesc(time_vector,freq_vector,20*log10(A));

where the first two inputs are vectors that you can define to set your axis. Similarly, for the phase:

imagesc(time_vector,phase_vector,phi);

Answer 2

If you create a volumetric (unflattened 3D) image, you can use 2 layers in the 3rd dimension to represent magnitude and phase, or real and imaginary components of a complex spectrogram output.

In a 2D color spectrogram, you could try using an orthogonal color mapping, for instance, in RGB space, red + green for magnitude and blue (or delta blue) for phase, or similar for real and imaginary components, or use YUV or HSL color spaces, etc.