Short-Time Fourier Transform (STFT) in Signal Processing - Mini Project: Build & Apply

Short-Time Fourier Transform (STFT) Analysis

📖 Scenario: You have recorded a short audio signal and want to analyze how its frequency content changes over time. This is useful in music, speech, and many other sound applications.

🎯 Goal: Build a simple program to compute the Short-Time Fourier Transform (STFT) of a signal using a sliding window and visualize the frequency changes over time.

📋 What You'll Learn

Create a sample signal as a list of numbers

Define a window size for the STFT

Compute the STFT by applying Fourier Transform on each window segment

Print the magnitude of the STFT result for each window

💡 Why This Matters

🌍 Real World

STFT is used in audio processing to analyze how sounds change over time, such as in music, speech recognition, and noise detection.

💼 Career

Understanding STFT helps in roles like audio engineer, data scientist working with time-series data, and anyone involved in signal processing.

1

Create the sample signal

Create a list called signal with these exact values: 0, 1, 0, -1, 0, 1, 0, -1, 0, 1

Signal Processing

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

Hint

Think of the signal as a simple wave repeating values.

2

Set the window size for STFT

Create a variable called window_size and set it to 4

Signal Processing

signal = [0, 1, 0, -1, 0, 1, 0, -1, 0, 1]
# Set the window size to 4
# Your code here

Hint

The window size decides how many samples you analyze at once.

3

Compute the STFT magnitude for each window

Import fft from numpy.fft. Create an empty list called stft_magnitudes. Use a for loop with variable start to slide over signal in steps of 1 until len(signal) - window_size + 1. Inside the loop, take a slice segment of signal[start:start + window_size], compute its Fourier Transform using fft(segment), then append the absolute values of the result to stft_magnitudes.

Signal Processing

signal = [0, 1, 0, -1, 0, 1, 0, -1, 0, 1]
window_size = 4
# Import fft and compute STFT magnitudes
# Your code here

Hint

Use a loop to slide the window and apply fft on each segment.

4

Print the STFT magnitudes

Use a for loop with variable i and magnitudes to iterate over enumerate(stft_magnitudes). Inside the loop, print the string "Window {i}: {magnitudes}" using an f-string.

Signal Processing

import numpy as np
from numpy.fft import fft

signal = [0, 1, 0, -1, 0, 1, 0, -1, 0, 1]
window_size = 4

stft_magnitudes = []
for start in range(len(signal) - window_size + 1):
    segment = signal[start:start + window_size]
    fft_result = fft(segment)
    magnitudes = np.abs(fft_result)
    stft_magnitudes.append(magnitudes)

# Print the STFT magnitudes for each window
# Your code here

Hint

Print each window number and its magnitude array using an f-string.