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 s
:
from scipy.fftpack import fft
sHat = fft(s)
Considering "the Fourier transform of white noise is white noise":
Can we generate sHat
directly without the Fourier-transform of s
?
I have recently tried to discuss a practical implementation of such thought herein.