Common window functions in Signal Processing - Mini Project: Build & Apply

Common Window Functions in Signal Processing

📖 Scenario: Imagine you are working on a project to analyze sound signals. To prepare the signals for analysis, you need to apply window functions. Window functions help reduce noise and improve the quality of the signal processing.

🎯 Goal: You will create a small program that generates three common window functions: rectangular, hamming, and hann. Then, you will display their values for a fixed window size.

📋 What You'll Learn

Create a dictionary with window names as keys and empty lists as values

Set a window size variable to 10

Fill the dictionary with values for rectangular, hamming, and hann windows using formulas

Print the dictionary with window names and their values

💡 Why This Matters

🌍 Real World

Window functions are used in audio and signal processing to reduce noise and improve analysis quality by shaping the signal before applying transformations like Fourier transforms.

💼 Career

Understanding and implementing window functions is important for roles in signal processing, audio engineering, and data analysis where clean signal data is crucial.

1

Create the window dictionary

Create a dictionary called windows with keys 'rectangular', 'hamming', and 'hann'. Set each key's value to an empty list.

Signal Processing

# Create the windows dictionary with empty lists
# Your code here

Hint

Use curly braces {} to create a dictionary. Each key should be a string and each value an empty list [].

2

Set the window size

Create a variable called window_size and set it to 10.

Signal Processing

windows = {'rectangular': [], 'hamming': [], 'hann': []}
# Set the window size to 10
# Your code here

Hint

Just assign the number 10 to the variable window_size.

3

Calculate window values

Use a for loop with variable n from 0 to window_size - 1. Inside the loop, calculate and append values for each window in windows using these formulas:

- Rectangular: 1
- Hamming: 0.54 - 0.46 * cos(2 * pi * n / (window_size - 1))
- Hann: 0.5 * (1 - cos(2 * pi * n / (window_size - 1)))

Use math.cos and math.pi. Import math at the top.

Signal Processing

import math

windows = {'rectangular': [], 'hamming': [], 'hann': []}
window_size = 10
# Calculate window values and append to lists
# Your code here

Hint

Use range(window_size) to loop from 0 to 9. Append values to each list inside the dictionary.

4

Print the window values

Print the windows dictionary to display the window names and their calculated values.

Signal Processing

import math

windows = {'rectangular': [], 'hamming': [], 'hann': []}
window_size = 10
for n in range(window_size):
    windows['rectangular'].append(1)
    windows['hamming'].append(0.54 - 0.46 * math.cos(2 * math.pi * n / (window_size - 1)))
    windows['hann'].append(0.5 * (1 - math.cos(2 * math.pi * n / (window_size - 1))))
# Print the windows dictionary
# Your code here

Hint

Use print(windows) to show the dictionary with all window values.