Encoding an image in to the fourier domain of a sound

I'm trying to convert an image to a sound where you can see the image if you were to view the spectrogram of that sound. Kind of like the aphex twin had done in window licker.

So far I have written an iPhone app that takes a photogra开发者_高级运维ph and then converts it to grayscale. I then use this gray scale as a magnitude which I'd like to plug back through an inverse FFT.

The problem I have, though, is how do I go from magnitude into the imaginary and real parts.

mag = sqrtf( (imag * imag) + (real * real));

Obviously I can't solve for 2 unknowns. Furthermore I can't find out if those real and imaginary parts are negative or not.

So I'm at a bit of a loss. It must be possible. Can anyone point me in the direction of some useful information?

A spectrogram contains no phase information, so you can just set the imaginary parts to 0 and set the real parts equal to the magnitude. Remember that you need to maintain complex conjugate symmetry if you want to end up with a purely real time domain signal after you have applied the inverse FFT.

The math wonks are right about regenerating from greyscale, but why limit yourself thus? Have you considered keeping a portion of the phase information in the color channels?

Specifically, why not process the LEFT channel into BLUE, the RIGHT channel into RED, and for the GREEN color element, run the transform again on (LEFT-RIGHT), so that you have three spectra.

In one version of "Surround Sound", L-R encodes the rear channel - there is good stuff there.

When regenerating your sound, assign the "real" values to the corresponding channels. Try the following (formulas - but this editor insists on calling them code..)

LEFT.real=+BLUE
RIGHT.real=+RED
LEFT.imag=+GREEN
RIGHT.imag=-GREEN

Experiment with variations on this, while listening thru some sort of surround sound setup, to see which provides the most pleasing results. Make sure not to drive the thing into clipping, since phase changes occur, regeneration of a complex saturated signal is likely to create clipping.