Common window functions in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Hann window values

What is the output array when applying a Hann window of length 5?

Signal Processing

import numpy as np
window = np.hanning(5)
print(window)

A [0. 0.25 1. 0.25 0. ]

B [0. 0.345 0.9 0.345 0. ]

C [0. 0.6545 1. 0.6545 0. ]

D [0. 0.5 1. 0.5 0. ]

💡 Hint

Recall the Hann window formula: w(n) = 0.5 * (1 - cos(2*pi*n/(N-1)))

The Hann window for length 5 produces values [0., 0.5, 1., 0.5, 0.].

🧠 Conceptual

intermediate

Purpose of window functions in signal processing

What is the main purpose of applying a window function to a signal before performing a Fourier transform?

A To remove noise from the signal completely

B To reduce spectral leakage by tapering the signal edges

C To convert the signal from time domain to frequency domain

D To increase the signal amplitude uniformly

💡 Hint

Think about what happens at the edges of a signal segment.

Window functions reduce spectral leakage by smoothing the edges of the signal segment before Fourier transform.

❓ data_output

advanced

Length of Blackman window output

What is the length of the output array when generating a Blackman window with parameter M=8?

Signal Processing

import numpy as np
window = np.blackman(8)
print(len(window))

A 9

B 7

C 8

D 10

💡 Hint

The window length equals the parameter M.

The Blackman window function returns an array of length equal to the input parameter M.

🔧 Debug

advanced

Identify error in window function code

What error will this code produce? import numpy as np window = np.hanning(-5) print(window)

Signal Processing

import numpy as np
window = np.hanning(-5)
print(window)

A ValueError: window length must be non-negative

B TypeError: unsupported operand type(s) for -: 'int' and 'str'

C SyntaxError: invalid syntax

D No error, outputs an empty array

💡 Hint

Check the parameter passed to np.hanning.

Negative window length is invalid and raises a ValueError.

🚀 Application

expert

Choosing window function for frequency resolution

You want to analyze a signal with closely spaced frequency components. Which window function is best to use to achieve the highest frequency resolution?

A Rectangular window

B Hamming window

C Blackman window

D Bartlett window

💡 Hint

Consider the trade-off between main lobe width and side lobe levels.

The rectangular window has the narrowest main lobe, giving the best frequency resolution but higher spectral leakage.

Practice

1. Which of the following window functions is known for having smooth edges and reducing spectral leakage in signal processing?

easy

A. Boxcar window

B. Rectangular window

C. Hamming window

D. Step window

Solution

1. Step 1: Understand window function purpose

   Window functions reduce spectral leakage by smoothing signal edges.

2. Step 2: Identify smooth edge windows

   Hamming window is designed with smooth edges to reduce leakage, unlike rectangular or step windows.

3. Final Answer:

   Hamming window -> Option C

4. Quick Check:

   Smooth edges = Hamming window [OK]

Hint: Smooth edges mean Hamming or Hann window, not rectangular [OK]

Common Mistakes:

• Confusing rectangular window as smooth
• Thinking step window reduces leakage
• Mixing boxcar with smooth windows

2. Which of the following is the correct Python syntax to generate a Hann window of length 64 using NumPy?

easy

A. np.hanning(64)

B. np.hamming(64)

C. np.hann(64)

D. np.window('hann', 64)

Solution

1. Step 1: Recall NumPy window function names

   NumPy uses np.hanning() to generate a Hann window, not np.hann().

2. Step 2: Check other options

   np.hamming() generates Hamming window, np.window() is invalid syntax.

3. Final Answer:

   np.hanning(64) -> Option A

4. Quick Check:

   Hann window in NumPy = np.hanning() [OK]

Hint: Hann window is np.hanning(), not np.hann() [OK]

Common Mistakes:

• Using np.hann() which does not exist
• Confusing Hamming and Hann functions
• Trying np.window() which is invalid

3. What is the output array when applying a Hamming window of length 4 using NumPy's np.hamming(4)?

medium

A. [0.0, 0.5, 0.5, 0.0]

B. [0.08, 0.77, 0.77, 0.08]

C. [1.0, 1.0, 1.0, 1.0]

D. [0.2, 0.6, 0.6, 0.2]

Solution

1. Step 1: Recall Hamming window formula

   Hamming window values for length 4 are approximately [0.08, 0.77, 0.77, 0.08].

2. Step 2: Verify with NumPy output

   Running np.hamming(4) returns array close to [0.08, 0.77, 0.77, 0.08].

3. Final Answer:

   [0.08, 0.77, 0.77, 0.08] -> Option B

4. Quick Check:

   np.hamming(4) ≈ [0.08, 0.77, 0.77, 0.08] [OK]

Hint: Small Hamming windows start and end near 0.08 [OK]

Common Mistakes:

• Assuming window starts at 0.0
• Confusing with rectangular window of all ones
• Mixing values with Hann window

4. The following code attempts to generate a Blackman window but throws an error. What is the error and how to fix it?

import numpy as np
window = np.blackman(32)

medium

A. AttributeError: np.blackman does not exist; use np.blackman_window(32)

B. TypeError: np.blackman expects two arguments

C. SyntaxError: missing parentheses in np.blackman(32)

D. AttributeError: np.blackman does not exist; use scipy.signal.blackman(32)

Solution

1. Step 1: Identify source of Blackman window

   NumPy does not have np.blackman; it's in scipy.signal as scipy.signal.blackman.

2. Step 2: Fix import and function call

   Import scipy.signal and call scipy.signal.blackman(32) to generate the window.

3. Final Answer:

   AttributeError: np.blackman does not exist; use scipy.signal.blackman(32) -> Option D

4. Quick Check:

   Blackman window in scipy.signal, not NumPy [OK]

Hint: Blackman window is in scipy.signal, not NumPy [OK]

Common Mistakes:

• Trying np.blackman which is not in NumPy
• Assuming syntax error instead of attribute error
• Using wrong function name np.blackman_window

5. You want to analyze a noisy signal segment of length 128 samples. Which window function should you apply before Fourier transform to minimize spectral leakage and why?

hard

A. Hamming window, because it reduces side lobes and smooths edges

B. Rectangular window, because it preserves signal amplitude exactly

C. Boxcar window, because it is the simplest and fastest

D. Step window, because it sharply cuts off signal edges

Solution

1. Step 1: Understand spectral leakage and window effects

   Spectral leakage occurs due to sharp edges; smooth windows reduce it.

2. Step 2: Choose window that reduces side lobes and smooths edges

   Hamming window is designed to reduce side lobes and smooth edges, minimizing leakage.

3. Final Answer:

   Hamming window, because it reduces side lobes and smooths edges -> Option A

4. Quick Check:

   Minimize leakage = use Hamming window [OK]

Hint: Use Hamming to smooth edges and reduce leakage [OK]

Common Mistakes:

• Choosing rectangular window which causes leakage
• Confusing boxcar with rectangular window
• Thinking step window helps reduce leakage