One can easily draw (pseudo-)random samples from a normal (Gaussian) distribution by using, say, NumPy:
import numpy as np mu, sigma = 0, 0.1 # mean and standard deviation s = np.random.normal(mu, sigma, 1000)
Now, consider the Fast Fourier transform of
from scipy.fftpack import fft sHat = fft(s)
Can we generate
sHat directly without the Fourier-transform of
I have recently tried to discuss a practical implementation of such thought herein.