Window functions in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Hamming window length

What is the length of the vector produced by the following MATLAB code?

win = hamming(10);
length_win = length(win);

MATLAB

win = hamming(10);
length_win = length(win);

A 1

B 9

C 11

D 10

💡 Hint

The hamming function creates a window vector with the specified length.

The hamming function with input 10 returns a column vector of length 10. So length(win) is 10.

❓ Predict Output

intermediate

Output of applying window to signal

What is the output of the following MATLAB code?

signal = ones(5,1);
win = hann(5);
result = signal .* win;

MATLAB

signal = ones(5,1);
win = hann(5);
result = signal .* win;

A [0; 0.5; 1; 0.5; 0]

B [1; 1; 1; 1; 1]

C [0.08; 0.54; 1; 0.54; 0.08]

D [0; 0.7071; 1; 0.7071; 0]

💡 Hint

The hann window values for length 5 are [0; 0.5; 1; 0.5; 0].

The hann window of length 5 produces values [0; 0.5; 1; 0.5; 0]. Multiplying by ones vector keeps these values.

❓ Predict Output

advanced

Output of Bartlett window sum

What is the sum of the Bartlett window vector generated by this code?

win = bartlett(5);
total = sum(win);

MATLAB

win = bartlett(5);
total = sum(win);

A 1.5

B 2

C 3

D 4

💡 Hint

Bartlett window is a triangular window starting and ending at zero.

bartlett(5) returns [0; 0.5; 1; 0.5; 0]. Sum is 2.

🧠 Conceptual

advanced

Effect of window length on frequency resolution

Which statement correctly describes how increasing the length of a window affects frequency resolution in signal processing?

A Increasing window length improves frequency resolution by narrowing the main lobe.

B Increasing window length decreases frequency resolution by widening the main lobe.

C Window length does not affect frequency resolution.

D Increasing window length increases side lobes but does not affect main lobe width.

💡 Hint

Think about how longer windows affect the sharpness of frequency components.

Longer windows produce narrower main lobes in the frequency domain, improving frequency resolution.

❓ Predict Output

expert

Output of custom window function code

What is the output of this MATLAB code?

n = 6;
w = zeros(n,1);
for k = 1:n
    w(k) = 0.5 - 0.5*cos(2*pi*(k-1)/(n-1));
end
w

MATLAB

n = 6;
w = zeros(n,1);
for k = 1:n
    w(k) = 0.5 - 0.5*cos(2*pi*(k-1)/(n-1));
end
w

A [0; 0.2; 0.5; 0.8; 1; 0.8]

B [0; 0.25; 0.5; 0.75; 1; 0.75]

C [0; 0.3455; 0.9045; 0.9045; 0.3455; 0]

D [0; 0.0955; 0.3455; 0.6545; 0.9045; 0]

💡 Hint

This formula matches the Hann window definition for length 6.

The formula computes the Hann window values for n=6, which are approximately [0; 0.3455; 0.9045; 0.9045; 0.3455; 0].

Practice

1. What is the primary purpose of using a window function in MATLAB signal processing?

easy

A. To reduce edge effects and smooth the signal

B. To increase the signal amplitude

C. To convert the signal from time to frequency domain

D. To generate random noise

Solution

1. Step 1: Understand window function role

   Window functions are used to taper the edges of a signal to reduce artifacts when processing.

2. Step 2: Identify the effect on signal

   They smooth the signal edges and reduce spectral leakage, not amplify or transform the signal.

3. Final Answer:

   To reduce edge effects and smooth the signal -> Option A

4. Quick Check:

   Window functions reduce edge effects [OK]

Hint: Window functions smooth edges to reduce artifacts [OK]

Common Mistakes:

• Thinking window functions amplify signals
• Confusing windowing with Fourier transform
• Assuming window functions add noise

2. Which of the following is the correct MATLAB syntax to create a Hamming window of length 64?

easy

A. hamming(64)

B. hamming[64]

C. window(hamming, 64)

D. window('hamming', 64)

Solution

1. Step 1: Recall MATLAB window function syntax

   MATLAB provides direct functions like hamming(N) to create windows of length N.

2. Step 2: Check each option

   hamming(64) uses correct function call syntax: hamming(64). window('hamming', 64) uses string incorrectly, C misses quotes, B uses wrong brackets.

3. Final Answer:

   hamming(64) -> Option A

4. Quick Check:

   Use hamming(N) to create Hamming window [OK]

Hint: Use hamming(N) directly, not window('hamming', N) [OK]

Common Mistakes:

• Using quotes incorrectly in function calls
• Using square brackets instead of parentheses
• Confusing window function with generic window()

3. What is the output size of the following MATLAB code?

win = blackman(100);
size_win = size(win);

medium

A. [1 100]

B. [100 100]

C. [100 1]

D. [1 1]

Solution

1. Step 1: Understand blackman output shape

   blackman(N) returns a column vector of length N, so size is N rows by 1 column.

2. Step 2: Apply to N=100

   Output is 100 rows and 1 column, so size is [100 1].

3. Final Answer:

   [100 1] -> Option C

4. Quick Check:

   blackman(N) returns column vector size [N 1] [OK]

Hint: Window functions return column vectors by default [OK]

Common Mistakes:

• Assuming output is a row vector
• Confusing size with length
• Expecting square matrix output

4. Identify the error in this MATLAB code snippet:

win = window('hann', 50);
plot(win);

medium

A. The 'hann' window is not supported in MATLAB

B. The plot function cannot plot window vectors

C. The window length must be greater than 100

D. The window function does not accept string arguments

Solution

1. Step 1: Check window function usage

   In MATLAB, window functions like hann are called directly, not via window('hann', N).

2. Step 2: Validate other options

   Plot can plot vectors, length 50 is valid, and 'hann' window is supported directly.

3. Final Answer:

   The window function does not accept string arguments -> Option D

4. Quick Check:

   Use hann(N), not window('hann', N) [OK]

Hint: Call hann(N) directly, not window('hann', N) [OK]

Common Mistakes:

• Using window() with string instead of direct function
• Thinking plot can't display vectors
• Assuming window length limits

5. You want to apply a Hamming window to a noisy signal vector sig of length 256 to reduce spectral leakage before FFT. Which MATLAB code correctly applies the window and computes the FFT?

hard

A. win = hamming(length(sig)); fft_sig = fft(sig + win);

B. win = hamming(256); fft_sig = fft(sig .* win);

C. win = hamming(256); fft_sig = fft(sig / win);

D. win = hamming(256); fft_sig = fft(sig - win);

Solution

1. Step 1: Create window matching signal length

   Use hamming(256) or hamming(length(sig)) to create the window vector.

2. Step 2: Apply window by element-wise multiplication

   Multiply signal by window element-wise to taper edges before FFT.

3. Step 3: Compute FFT of windowed signal

   Use fft(sig .* win) to get frequency spectrum of windowed signal.

4. Final Answer:

   win = hamming(256); fft_sig = fft(sig .* win); -> Option B

5. Quick Check:

   Window applied by multiplication before FFT [OK]

Hint: Multiply signal by window before FFT [OK]

Common Mistakes:

• Adding or subtracting window instead of multiplying
• Dividing signal by window
• Using window length different from signal length