Windowing before FFT in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the Hann window function from scipy.signal.

SciPy

from scipy.signal import [1]

Drag options to blanks, or click blank then click option'

Ahamming

Bblackman

Chann

Dbartlett

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the wrong window function like hamming or blackman.

Misspelling the function name.

The Hann window is imported from scipy.signal as hann.

2fill in blank

medium

Complete the code to create a Hann window of length 256.

SciPy

window = hann([1])

Drag options to blanks, or click blank then click option'

A128

B1024

C512

D256

Attempts:

3 left

💡 Hint

Common Mistakes

Using a window length different from the signal length.

Confusing window length with FFT length.

The window length should match the signal length, here 256.

3fill in blank

hard

Fix the error in applying the window to the signal array named 'signal'.

SciPy

windowed_signal = signal [1] window

Drag options to blanks, or click blank then click option'

A+

B*

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Adding or subtracting the window instead of multiplying.

Dividing the signal by the window.

Windowing is done by multiplying the signal by the window element-wise.

4fill in blank

hard

Fill the blank to compute the FFT of the windowed signal and get its magnitude.

SciPy

fft_result = np.fft.[1](windowed_signal)
magnitude = np.abs(fft_result)

Drag options to blanks, or click blank then click option'

Afft

Bifft

Creal

Dimag

Attempts:

3 left

💡 Hint

Common Mistakes

Using inverse FFT instead of FFT.

Trying to get magnitude by accessing .real or .imag.

Use np.fft.fft to compute the FFT and np.abs to get the magnitude.

5fill in blank

hard

Fill all three blanks to create a windowed signal, compute its FFT, and plot the magnitude spectrum.

SciPy

import matplotlib.pyplot as plt

window = hann([1])
signal = np.sin(2 * np.pi * 5 * np.arange([2]) / [3])
windowed_signal = signal * window
fft_result = np.fft.fft(windowed_signal)
magnitude = np.abs(fft_result)
plt.plot(magnitude)
plt.title('Magnitude Spectrum')
plt.xlabel('Frequency Bin')
plt.ylabel('Magnitude')
plt.show()

Drag options to blanks, or click blank then click option'

A256

B100

D512

Attempts:

3 left

💡 Hint

Common Mistakes

Using different lengths for window and signal.

Not matching the range length with window length.

The window length and signal length must match (256). The signal is created with 256 points.

Practice

1. What is the main purpose of applying a window function to a signal before performing an FFT?

easy

A. To increase the signal amplitude

B. To reduce spectral leakage by smoothing signal edges

C. To convert the signal from time domain to frequency domain

D. To remove noise from the signal

Solution

1. Step 1: Understand spectral leakage in FFT

   Spectral leakage occurs when the signal edges are abrupt, causing spreading of frequency components.

2. Step 2: Role of window functions

   Window functions smooth the edges of the signal to reduce this leakage before FFT.

3. Final Answer:

   To reduce spectral leakage by smoothing signal edges -> Option B

4. Quick Check:

   Windowing reduces leakage = B [OK]

Hint: Windowing smooths edges to reduce leakage before FFT [OK]

Common Mistakes:

• Thinking windowing increases amplitude
• Confusing windowing with noise removal
• Believing windowing converts domains

2. Which of the following is the correct way to create a Hann window of length 256 using scipy?

easy

A. window = scipy.signal.hann(256)

B. window = scipy.get_window('hann', 256)

C. window = scipy.signal.window('hann', 256)

D. window = scipy.signal.get_window('hann', 256)

Solution

1. Step 1: Identify the correct scipy module and function

   The function to create windows is get_window inside scipy.signal.

2. Step 2: Check syntax for get_window

   Correct syntax is scipy.signal.get_window(window_name, length).

3. Final Answer:

   window = scipy.signal.get_window('hann', 256) -> Option D

4. Quick Check:

   Use scipy.signal.get_window('hann', length) = D [OK]

Hint: Use scipy.signal.get_window('hann', length) to create Hann window [OK]

Common Mistakes:

• Using scipy.get_window instead of scipy.signal.get_window
• Calling nonexistent scipy.signal.window function
• Using scipy.signal.hann which does not exist

3. What is the output of the following code snippet?

import numpy as np
from scipy.signal import get_window

signal = np.ones(4)
window = get_window('hann', 4)
windowed_signal = signal * window
print(np.round(windowed_signal, 3))

medium

A. [0. 0.75 0.75 0. ]

B. [0. 0.5 0.5 0. ]

C. [0. 1. 1. 0. ]

D. [1. 1. 1. 1.]

Solution

1. Step 1: Calculate the Hann window values for length 4

   The Hann window for length 4 is [0, 0.75, 0.75, 0].

2. Step 2: Multiply the signal by the window element-wise

   Signal is all ones, so windowed_signal equals the window values.

3. Final Answer:

   [0. 0.75 0.75 0. ] -> Option A

4. Quick Check:

   Hann window at length 4 = [0, 0.75, 0.75, 0] [OK]

Hint: Hann window starts and ends at 0, peaks near middle [OK]

Common Mistakes:

• Assuming window values are 0.5 instead of 0.75
• Forgetting to multiply element-wise
• Confusing Hann with rectangular window

4. Identify the error in the following code that applies a Hamming window before FFT:

import numpy as np
from scipy.signal import get_window

signal = np.array([1, 2, 3, 4, 5])
window = get_window('hamming', 5)
windowed_signal = signal + window
fft_result = np.fft.fft(windowed_signal)
print(np.round(np.abs(fft_result), 2))

medium

A. Window should be multiplied, not added, to the signal

B. The window length must be larger than the signal length

C. np.fft.fft cannot be used on windowed signals

D. Hamming window cannot be created with length 5

Solution

1. Step 1: Check how window is applied to signal

   The code adds the window to the signal instead of multiplying element-wise.

2. Step 2: Correct application of window

   Windowing requires element-wise multiplication to smooth edges before FFT.

3. Final Answer:

   Window should be multiplied, not added, to the signal -> Option A

4. Quick Check:

   Windowing = element-wise multiply, not add [OK]

Hint: Always multiply signal by window, never add [OK]

Common Mistakes:

• Adding window instead of multiplying
• Assuming window length must exceed signal length
• Thinking FFT can't be applied after windowing

5. You have a noisy signal sampled at 1000 Hz with 1024 points. You want to analyze its frequency content using FFT with minimal spectral leakage. Which steps correctly apply windowing before FFT using scipy?

hard

A. Create a Hamming window of length 512, multiply it with the first half of the signal, then compute FFT

B. Create a rectangular window, add it to the signal, then compute FFT

C. Create a Hann window of length 1024, multiply it element-wise with the signal, then compute FFT

D. Compute FFT directly without windowing to preserve original signal

Solution

1. Step 1: Choose appropriate window and length

   Hann window is common for reducing spectral leakage; length must match signal length (1024).

2. Step 2: Apply window and compute FFT

   Multiply signal element-wise by window, then compute FFT on the windowed signal.

3. Final Answer:

   Create a Hann window of length 1024, multiply it element-wise with the signal, then compute FFT -> Option C

4. Quick Check:

   Window length = signal length, multiply before FFT = A [OK]

Hint: Match window length to signal, multiply before FFT [OK]

Common Mistakes:

• Adding window instead of multiplying
• Using wrong window length
• Skipping windowing and accepting leakage