"""
======================================
Spectrogram, power spectral density
======================================

Demo spectrogram and power spectral density on a frequency chirp.

Taken from https://scipy-lectures.org/intro/scipy/auto_examples/plot_spectrogram.html#sphx-glr-intro-scipy-auto-examples-plot-spectrogram-py.
"""

import numpy as np
from matplotlib import 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)

############################################################
# Compute and plot the spectrogram
############################################################
#
# The spectrum of the signal on consecutive time windows

from scipy import signal
freqs, times, spectrogram = 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 = 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()



