51 lines
1.1 KiB
Python
51 lines
1.1 KiB
Python
|
import matplotlib.pyplot as plt
|
||
|
|
import numpy as np
|
||
|
|
from numpy import random
|
||
|
|
import scipy.signal as sgl
|
||
|
|
|
||
|
|
yi = random.normal(size=2**20)
|
||
|
|
yr = 0.3 * np.roll(yi, -(2**10))
|
||
|
|
|
||
|
|
figy, axy = plt.subplots()
|
||
|
|
axy.plot(np.arange(2**10, 2**11), yi[2**10 : 2**11])
|
||
|
|
axy.plot(np.arange(2**10, 2**11), yr[2**10 : 2**11])
|
||
|
|
|
||
|
|
figf, axf = plt.subplots()
|
||
|
|
axf.plot(*sgl.welch(yi))
|
||
|
|
axf.plot(*sgl.welch(yr))
|
||
|
|
|
||
|
|
eta = yi + yr
|
||
|
|
u = -yi + yr
|
||
|
|
|
||
|
|
|
||
|
|
def puv(eta, u):
|
||
|
|
f, phi_eta = sgl.welch(eta)
|
||
|
|
phi_u = sgl.welch(u)[1]
|
||
|
|
phi_eta_u = np.abs(sgl.csd(eta, u)[1].real)
|
||
|
|
|
||
|
|
return f, np.sqrt(
|
||
|
|
(phi_eta + phi_u - 2 * phi_eta_u) / (phi_eta + phi_u + 2 * phi_eta_u)
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
figr, axr = plt.subplots()
|
||
|
|
|
||
|
|
axr.plot(*puv(eta, u), label="Without noise")
|
||
|
|
axr.plot(
|
||
|
|
*puv(
|
||
|
|
eta + 0.4 * random.normal(size=2**20), u + 0.4 * random.normal(size=2**20)
|
||
|
|
),
|
||
|
|
label="With noise"
|
||
|
|
)
|
||
|
|
axr.grid()
|
||
|
|
axr.autoscale(True, "x", tight=True)
|
||
|
|
axr.set(ylim=(0, 1), ylabel="R", xlabel="f")
|
||
|
|
axr.legend(loc="lower left")
|
||
|
|
|
||
|
|
axpsd = axr.twinx()
|
||
|
|
axpsd.plot(*sgl.welch(eta), label=r"PSD ($\eta$)", c="k", alpha=0.2, lw=1)
|
||
|
|
axpsd.legend(loc="lower right")
|
||
|
|
axpsd.set(ylabel="PSD")
|
||
|
|
|
||
|
|
plt.show()
|