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Although the author couldn't do it, the problem is obviously solvable, and not even that difficult.

Theory: https://rjav.sra.ro/index.php/rjav/article/view/40/29 [PDF]

Matlab code (under the Functions tab): https://www.mathworks.com/matlabcentral/fileexchange/42919-p...

This is for the 1D case, but since the Fourier transform is separable, it works identically in 2 (and any N) dimensions by performing the transform sequentially in every dimensions.

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Does that approach end up with a uniform distribution if values in the time domain? That seemed like the difficult part here.

You're pointing to something saying that power-law distributed noise can be generated by filtering white noise (and doing the filtering in the frequency domain, but that's really an implementation detail). OP actually wants to only do the inverse transform, generating the noise in the frequency domain already.

The Fourier transform of white noise is white noise, so that doesn't matter.

Ah hm seems legit, didn't think it through. Weird why OP didn't manage then..

Because he is confusing the sample frequencies with the frequencies of the autocorelation.

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