import numpy as np
from matplotlib.pylab import *

t, n1, n2, n3 = np.load('simulation.npy')

def gauss(x, mu=0.0, sigma=1.0):
    return 1.0/(sigma*np.sqrt(2.0*np.pi)) * np.exp(-0.5 * ((x-mu)/sigma)**2)

def fold(A, B):
    N = max(len(A), len(B))
    Ahat = np.fft.rfft(A,N)
    Bhat = np.fft.rfft(B,N)
    prod = ((-1.0)**arange(len(Ahat))) / N * Ahat * Bhat 
    folded = np.fft.irfft(prod, N)
    return folded

N = len(t)
T = t[-1]-t[0]

g1 = gauss(t-T/2, sigma=100.0)
s1 = fold(n2, g1) * T
s1[:10] = np.NaN
s1[-10:] = np.NaN

g2 = gauss(t-T/2, sigma=1000.0)
s2 = fold(n2, g2) * T
s2[:100] = np.NaN
s2[-100:] = np.NaN

g3 = gauss(t-T/2, sigma=10000.0)
s3 = fold(n2, g3) * T
s3[:1000] = np.NaN
s3[-1000:] = np.NaN

figure()
plot(t, n2, '.')
plot(t, s1, linewidth=2)
plot(t, s2, linewidth=2)
plot(t, s3, linewidth=2)

show()