Plotting Coherence of Two Signals

Introduction

This lab demonstrates how to plot the coherence of two signals using Python's Matplotlib library. The coherence of two signals is a measure of their linear relationship, with a value of 1 indicating perfect coherence and a value of 0 indicating no coherence.

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Import Libraries

The first step is to import the necessary libraries. We will be using NumPy and Matplotlib.

import matplotlib.pyplot as plt
import numpy as np

Generate Signals

Next, we will generate two signals with a coherent part at 10 Hz and a random part. We will also add white noise to the signals.

## Fixing random state for reproducibility
np.random.seed(19680801)

dt = 0.01
t = np.arange(0, 30, dt)
nse1 = np.random.randn(len(t))                 ## white noise 1
nse2 = np.random.randn(len(t))                 ## white noise 2

s1 = np.sin(2 * np.pi * 10 * t) + nse1
s2 = np.sin(2 * np.pi * 10 * t) + nse2

Plot Signals

We can now plot the two signals in the time domain using Matplotlib.

fig, axs = plt.subplots(2, 1)
axs[0].plot(t, s1, t, s2)
axs[0].set_xlim(0, 2)
axs[0].set_xlabel('Time')
axs[0].set_ylabel('s1 and s2')
axs[0].grid(True)

Plot Coherence

We can now plot the coherence of the two signals using Matplotlib's cohere function.

cxy, f = axs[1].cohere(s1, s2, 256, 1. / dt)
axs[1].set_ylabel('Coherence')

Display Plot

Finally, we can display the plot using Matplotlib's show function.

fig.tight_layout()
plt.show()

Summary

This lab demonstrated how to plot the coherence of two signals using Python's Matplotlib library. We generated two signals with a coherent part at 10 Hz and a random part, added white noise to the signals, and plotted the signals in the time domain and their coherence using Matplotlib's cohere function.