"""

Compute the cross spectral density of two signals

"""

import numpy as np

import matplotlib.pyplot as plt

fig, (ax1, ax2) = plt.subplots(2, 1)

# make a little extra space between the subplots

fig.subplots_adjust(hspace=0.5)

dt = 0.01

t = np.arange(0, 30, dt)

nse1 = np.random.randn(len(t)) # white noise 1

nse2 = np.random.randn(len(t)) # white noise 2

r = np.exp(-t/0.05)

cnse1 = np.convolve(nse1, r, mode='same')*dt # colored noise 1

cnse2 = np.convolve(nse2, r, mode='same')*dt # colored noise 2

# two signals with a coherent part and a random part

s1 = 0.01*np.sin(2*np.pi*10*t) + cnse1

s2 = 0.01*np.sin(2*np.pi*10*t) + cnse2

ax1.plot(t, s1, t, s2)

ax1.set_xlim(0, 5)

ax1.set_xlabel('time')

ax1.set_ylabel('s1 and s2')

ax1.grid(True)

cxy, f = ax2.csd(s1, s2, 256, 1./dt)

ax2.set_ylabel('CSD (db)')

plt.show()