import numpy as np
import scipy.signal as sig
import scipy.optimize as op

import matplotlib.pyplot as plt
from matplotlib import rc;
rc("text"   ,usetex=True)
rc("text.latex", unicode=True)

N = 10000
n = 100

rng1 = np.random.normal(size=N)
rng2 = np.asarray(np.random.normal(size=N),dtype=np.int)

xs = np.linspace(1,n,n,dtype=np.int)
errs1, errs2 = np.zeros(n), np.zeros(n)
for i in xs:
    win = sig.exponential(i*20+1, tau=i, sym=1)
    r1 = np.convolve(rng1, win/i, mode="same")
    r2 = np.convolve(rng2, win/i, mode="same")
    errs1[i-1] = np.std(r1)
    errs2[i-1] = np.std(r2)

fig,ax = plt.subplots()
ax.plot(xs,errs1,"-r",label="$\sigma_f$")
ax.plot(xs,errs2,"-b",label="$\sigma_i$")
#ax.plot(xs,errs1/errs2,"-k",label="$\sigma_f/\sigma_i$")
ax.legend()
ax.set_xlim(xs[0],xs[-1])

plt.show()