import numpy as np
import math
import matplotlib.pyplot as plt

N = 512
L = 3
sigma2 = 1
Scatter = 100
Cov = 10
n = 1
f = []
x = []
y = []
F = []
cov = np.zeros(Cov)
e = np.zeros(L)

h = [1,3,2]
       
def setf(f,h,e):
    f.clear()
    e = np.zeros(L)
    for i in range(N):
      e[0] = np.random.normal(0,1)
      f.append(sum([h[j]*e[j] for j in range(L)]))
      e = np.roll(e,1)

for i in range(Scatter):
    setf(f,h,e)
    x.append(f[100])
    y.append(f[100+n])

for k in range(Cov):
    if k >= L :
        cov[k] = 0
    else:
        cov[k] = 0
        for i in range(k,L):
            cov[k] += h[i]*h[i-k]
        cov[k] *= sigma2
    
for i in range(int(N/2)):
    th = 2*math.pi*i/N;
    re = h[0] + sum([h[j]*math.cos(-j*th) for j in range(1,L)])
    im =        sum([h[j]*math.sin(-j*th) for j in range(1,L)])
    F.append(np.abs(re+im*1j))

fft = np.fft.fft(f)/np.sqrt(N)
    
plt.xlim([0,N-1])
plt.plot(f)
plt.show()

plt.xlim([0,Cov-1])
plt.plot(cov,'-o')
plt.show()

plt.scatter(x,y)
plt.xlabel("f [100]")
plt.ylabel("f [{}]".format(100+n))
plt.show()

plt.xlim([0,N/2-1])
plt.plot(np.abs(fft))
plt.plot(F)
plt.show()