File:Bartlett's method.svg

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt

Nsub = 100  # number of subsequences

w_1 = 30  # frequency of 1st component of  signal (Hz)
w_2 = 40  # frequency of 2nd component of signal (Hz)

a = 0.7  # magnitude of 1st component of signal
b = 0.4  # magnitude of  2nd component of signal

t = np.array([i for i in range(1, 301)]) / 1000  # time samples (s)
fs = 1 / (t[1] - t[0])  # sampling frequency (Hz)

x = a * np.cos(2 * np.pi * w_1 * t) + b * np.sin(2 * np.pi * w_2 * t)  # considered signal

y_mat = np.dot(np.ones((Nsub, 1)), x.reshape((1, len(x))))  # assume subsequences are identical

f = []
Pxx = np.empty((Nsub, int((len(x) / 2) + 1)))
for i in range(np.shape(y_mat)[0]):
    y_mat[i, :] = y_mat[i, :]
    f, Pxx[i, :] = signal.periodogram(y_mat[i, :], fs=fs, scaling='spectrum')
Pxx_bart = np.mean(Pxx, axis=0)

plt.subplots(1, 1, figsize=(6, 4), dpi=250)
plt.stem(f[1:20], Pxx_bart[1:20], '-')
plt.ylabel('Spectrum')
plt.xlabel('Frequencies (Hz)')
plt.title('Bartlett\'s method')
plt.grid(True)
plt.savefig("Bartett's method.svg", format="svg")