Xcorr Acorr Demo

Introduction

The purpose of this lab is to demonstrate the use of cross-correlation and auto-correlation plots using the Python Matplotlib library. Cross-correlation and auto-correlation are mathematical tools used to measure the similarity between two signals. Cross-correlation measures the similarity between two different signals, while auto-correlation measures the similarity between a signal and a time-delayed version of itself. These tools are commonly used in signal processing, image analysis, and time series analysis.

VM Tips

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Import Libraries

First, we need to import the necessary libraries. In this lab, we will be using NumPy and Matplotlib.

import matplotlib.pyplot as plt
import numpy as np

Generate Random Data

Next, we will generate two arrays of random data using NumPy. We will use these arrays to demonstrate cross-correlation and auto-correlation.

np.random.seed(19680801)
x, y = np.random.randn(2, 100)

Plot Cross-Correlation

We will now plot the cross-correlation between the two arrays using the xcorr function in Matplotlib.

fig, ax = plt.subplots()
ax.xcorr(x, y, usevlines=True, maxlags=50, normed=True, lw=2)
ax.grid(True)
plt.show()

The xcorr function takes the following parameters:

• x: the first array of data
• y: the second array of data
• usevlines: boolean, whether to plot vertical lines from 0 to the correlation value
• maxlags: integer, the maximum number of lags to calculate the correlation for
• normed: boolean, whether to normalize the correlation values
• lw: integer, the line width for the plot

Plot Auto-Correlation

We will now plot the auto-correlation of the x array using the acorr function in Matplotlib.

fig, ax = plt.subplots()
ax.acorr(x, usevlines=True, normed=True, maxlags=50, lw=2)
ax.grid(True)
plt.show()

The acorr function takes the following parameters:

• x: the array of data to calculate the auto-correlation for
• usevlines: boolean, whether to plot vertical lines from 0 to the correlation value
• normed: boolean, whether to normalize the correlation values
• maxlags: integer, the maximum number of lags to calculate the correlation for
• lw: integer, the line width for the plot

Summary

In this lab, we learned how to use cross-correlation and auto-correlation plots in Python Matplotlib. We first imported the necessary libraries, then generated random data using NumPy. We then plotted the cross-correlation and auto-correlation of the data using the xcorr and acorr functions in Matplotlib. These tools are useful for measuring the similarity between two signals and are commonly used in signal processing, image analysis, and time series analysis.