N = 128
x = np.arange(-5, 5, 10.0 / (2 * N))
y = np.exp(-x * x)
y_fft = np.fft.fftshift(np.abs(np.fft.fft(y))) / np.sqrt(2 * N)
plt.plot(x, y)
plt.plot(x, y_fft)
plt.show()
Fourier transform of a Gaussian is not a Gaussian, but thats wrong! - Python