Power spectral density estimation in Signal Processing - Mini Project: Build & Apply

Power Spectral Density Estimation

📖 Scenario: You have recorded a simple signal from a sensor over time. You want to understand how the signal's power is spread across different frequencies. This helps in identifying dominant frequencies or noise in the signal.

🎯 Goal: Build a small program to estimate the power spectral density (PSD) of a given signal using the periodogram method. You will create the signal data, set the sampling frequency, compute the PSD, and then display the frequency and power values.

📋 What You'll Learn

Create a time-domain signal as a list of values

Define the sampling frequency as a variable

Use the periodogram method to compute the power spectral density

Print the frequency array and the corresponding power spectral density values

💡 Why This Matters

🌍 Real World

Power spectral density estimation is used in engineering and science to analyze signals like sound, vibrations, or electrical signals to find dominant frequencies or noise.

💼 Career

Understanding PSD helps in roles like signal processing engineer, data analyst, or any job involving sensor data analysis and noise filtering.

1

Create the signal data

Create a list called signal with these exact values: 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -1.0

Signal Processing

# Create the signal list with the given values
# Your code here

Hint

This signal represents a simple repeating pattern over time.

2

Set the sampling frequency

Create a variable called fs and set it to 4 to represent the sampling frequency in Hertz

Signal Processing

signal = [0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -1.0]
# Set the sampling frequency fs to 4
# Your code here

Hint

The sampling frequency tells how many samples are taken per second.

3

Compute the power spectral density

Import periodogram from scipy.signal and use it with signal and fs to compute frequencies and power

Signal Processing

signal = [0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -1.0]
fs = 4
# Import periodogram and compute frequencies and power
# Your code here

Hint

The periodogram function returns two arrays: frequencies and power spectral density values.

4

Display the power spectral density

Print the frequencies array and the power array each on a separate line

Signal Processing

from scipy.signal import periodogram

signal = [0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, -1.0]
fs = 4

frequencies, power = periodogram(signal, fs)
# Print frequencies and power arrays
# Your code here

Hint

Printing these arrays shows how power is distributed across frequencies.