this is more of a theoretical question as the implementation doesn't really matter.
I'm experimenting in Matlab, and I was curious about something. I know that the division of Gaussian-distributed random variates (with mean = 0) results in a Cauchy distribution.
(See here: Normal Ratio Distribution on Wolfram Mathworld)
But if I take the Fourier Transform of each Gaussian-distribution from which I'm getting my variates, is that equal to the Fourier Transform of a Cauchy distribution?
i.e. Is fft(G1)/fft(G2) = fft(equivalent Cauchy)
If not, how do I model the ratio of two normally distributed variates in the frequency domain?