Windowing before FFT in SciPy - Mini Project: Build & Apply

Windowing before FFT

📖 Scenario: You have recorded a short sound signal and want to analyze its frequency content. To get better results, you will apply a window function before computing the Fast Fourier Transform (FFT).

🎯 Goal: Learn how to apply a window function to a signal before performing FFT to reduce spectral leakage and visualize the frequency spectrum.

📋 What You'll Learn

Create a signal array with exact values

Create a window array using a Hamming window

Multiply the signal by the window

Compute the FFT of the windowed signal

Print the magnitude of the FFT result

💡 Why This Matters

🌍 Real World

Windowing before FFT is used in audio processing, vibration analysis, and any signal processing to get clearer frequency results.

💼 Career

Understanding windowing and FFT is essential for roles in data science, signal processing, and engineering fields involving time-series data.

1

Create the signal array

Create a NumPy array called signal with these exact values: [0, 1, 0, -1, 0, 1, 0, -1].

SciPy

import numpy as np
# Create the signal array called signal with values [0, 1, 0, -1, 0, 1, 0, -1]
# Your code here

Need a hint?

Use np.array to create the array with the exact values.

2

Create the Hamming window

Create a variable called window that holds a Hamming window of the same length as signal using np.hamming(len(signal)).

SciPy

import numpy as np
signal = np.array([0, 1, 0, -1, 0, 1, 0, -1])
# Create the Hamming window called window with length equal to signal
# Your code here

Need a hint?

Use np.hamming with the length of signal to create the window.

3

Apply the window and compute FFT

Create a variable called windowed_signal by multiplying signal and window element-wise. Then create a variable called fft_result by computing the FFT of windowed_signal using np.fft.fft(windowed_signal).

SciPy

import numpy as np
signal = np.array([0, 1, 0, -1, 0, 1, 0, -1])
window = np.hamming(len(signal))
# Multiply signal and window element-wise to create windowed_signal
# Compute FFT of windowed_signal and store in fft_result
# Your code here

Need a hint?

Multiply arrays element-wise with *. Use np.fft.fft to compute the FFT.

4

Print the magnitude of the FFT result

Print the magnitude (absolute value) of fft_result using print(np.abs(fft_result)).

SciPy

import numpy as np
signal = np.array([0, 1, 0, -1, 0, 1, 0, -1])
window = np.hamming(len(signal))
windowed_signal = signal * window
fft_result = np.fft.fft(windowed_signal)
# Print the magnitude of fft_result
# Your code here

Need a hint?

Use np.abs() to get the magnitude of complex FFT results.