It's a log power spectrum (or log abs spectrum) that is being displayed, so you can get away with only adding the pixel values to the real part. There are probably cleaner ways to do it soundwise to avoid high frequency noise, but it would get the job done.
I think it would be interesting to embed these types of things as the difference between left and right channels (or channels of 5.1 surround), so that it could only be seen by subtracting the two channels then doing the log power spectrum. Lots of fun!
Showing (L-R) of the Fourier magnitude is actually one of the settings I like to use when showing music in baudline[1]. I use it to see how some songs utilize the audio spectrum and stereo effects a lot easier to see when showing the difference between the channels instead of the usual side-by-side.
I wonder what it would look like to encode the phase as a hue rotation (HSV). Probably a mess of colors in most cases, I would guess.
It was just an idea - the only advantage might be that you could easily see the whole frequency spectrum at the same time instead of having to infer it from the lissajous pattern. It probably isn't that useful most of the time. Baudline can show you magnitude with phase as different colors (or real+imaginary), but that can blur together sometimes.
A goniometer is super-useful during synthesis. The recent(-ish) versions of sunvox[1] lets you put a goniometer on any module in the synthesis chain; I love being able to see stuff like the phase of a delay effect.
I think it would be interesting to embed these types of things as the difference between left and right channels (or channels of 5.1 surround), so that it could only be seen by subtracting the two channels then doing the log power spectrum. Lots of fun!