1.5.12.9. Spectrogram, power spectral density

Demo spectrogram and power spectral density on a frequency chirp.

import numpy as np
import matplotlib.pyplot as plt

Generate a chirp signal

# Seed the random number generator
np.random.seed(0)

time_step = .01
time_vec = np.arange(0, 70, time_step)

# A signal with a small frequency chirp
sig = np.sin(0.5 * np.pi * time_vec * (1 + .1 * time_vec))

plt.figure(figsize=(8, 5))
plt.plot(time_vec, sig)

[<matplotlib.lines.Line2D object at 0x7fe7b04e1310>]

Compute and plot the spectrogram

The spectrum of the signal on consecutive time windows

import scipy as sp
freqs, times, spectrogram = sp.signal.spectrogram(sig)

plt.figure(figsize=(5, 4))
plt.imshow(spectrogram, aspect='auto', cmap='hot_r', origin='lower')
plt.title('Spectrogram')
plt.ylabel('Frequency band')
plt.xlabel('Time window')
plt.tight_layout()

Compute and plot the power spectral density (PSD)

The power of the signal per frequency band

freqs, psd = sp.signal.welch(sig)

plt.figure(figsize=(5, 4))
plt.semilogx(freqs, psd)
plt.title('PSD: power spectral density')
plt.xlabel('Frequency')
plt.ylabel('Power')
plt.tight_layout()

plt.show()