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

w_1 = 40 # frequency of the 1st component of the signal (Hz)
w_2 = 60 # frequency of the 2nd component of the signal (Hz)

a = 0.5 # magnitude of the 1st component of the signal
b = 1.0 # magnitude of the 2nd component of the 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
n = .2*np.random.randn(len(t)) # white Gaussian noise
y = x + n

windows = [None,'hamming']
plt.subplots(1, 1, figsize=(6, 4), dpi=250)

for window in windows:
    if window == None:
        label = 'rect'
    else:
        label = window
    f, Pxx_den = signal.periodogram(y, fs=fs, scaling='spectrum', nfft=2048, window=window)
    plt.semilogy(f[1:200], Pxx_den[1:200], label=label)

plt.subplots(1, 1, figsize=(6, 4), dpi=250)
plt.ylabel('Spectrum')
plt.xlabel('Frequencies (Hz)')
plt.title('Periodogram')
plt.grid(True)
plt.show()