This is related to this Nice answer by the thread
What is the Fourier transform of $f(x)=e^{-x^2}$?.
Considering this derivation of fourier transform of Gaussian with mean 0 and unit variance, why do we get complex data type when I take fourier transform of AWGN (Addititive white gaussian noise) ?. (You can try in matlab by taking FFT of awgn function.)
"""
no_sig = zeros(128,256);
no_sig_noise = awgn(no_sig,0);
no_sig_fft = fft2(no_sig_noise);
"""
if you observe no_sig_fft, it has complex form (a+jb). My question is : As per the derivation, the Fourier transform of Gaussian distributed data is : $e^{-w^2/4}$ , which will give real data. But when i do fft of AWGN, i get complex data ($a+jb$). Why is this so. Anything i have missed in understanding?