[stochtastic]

There is an interesting relationship between frequency domain filtering and the distributional properties of a signal, which I believe the author encounters:

  So interestingly, the IDFT method makes noise that is gaussian distributed. This kind of makes sense because we are filling out frequencies as uniform random white noise, which are turning into uniform random white noise sinusoids that are being summed together, which will tend towards a gaussian distribution as you sum up more of them. In contrast, the void and cluster method makes uniform distributed values which are perfectly uniform.

One of the papers I'm most proud of co-authoring explains some aspects of this phenomenon [0] through the use of higher order spectra (the bispectrum, trispectrum, etc...) and how the geometry of frequency-domain filters affects skewness and excess kurtosis.

[0] https://s3-us-west-2.amazonaws.com/arpdfs/Publications/Prois...

[a9h74j]

FWIW, in looking up higher-order spectra, I see that work at LIGO has resulted in an interesting toolkit and documentation:

https://labcit.ligo.caltech.edu/~rana/mat/HOSA/HOSA.PDF