In [22]:

    

from numpy import linspace, sqrt, pi,exp, angle
from numpy.fft import fft,ifft,fftshift
from matplotlib.pyplot import subplots,show

x = linspace(-15,15,200)
w = linspace(-pi, pi,200)
sigma = 1

g = 1/(sigma*sqrt(2*pi)) * exp(-(x-0)**2/(2*sigma**2))
G = fft(g)

Gana = exp(-w**2 * sigma**2/2)

fg,ax = subplots(4,1)
ax[0].plot(x,g)
ax[0].set_title('g(x)')
ax[0].set_xlabel('x')

ax[1].plot(w, abs(fftshift(G)),label='G($\omega$)')
ax[2].plot(1/2*pi*w, abs(Gana), label='$G_{analytic}$')
ax[2].set_xlim((-pi,pi))

ax[3].plot(G.imag)

show()


    

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