Window functions in MATLAB - Mini Project: Build & Apply

Using Window Functions in MATLAB

📖 Scenario: You are working on a signal processing project. You need to apply a window function to a signal to reduce spectral leakage before performing a Fourier transform.

🎯 Goal: Learn how to create a signal, generate a window function, apply the window to the signal, and display the result.

📋 What You'll Learn

Create a signal vector with specific values

Create a window function vector using the Hamming window

Apply the window function to the signal by element-wise multiplication

Display the original and windowed signals

💡 Why This Matters

🌍 Real World

Window functions are used in signal processing to reduce artifacts when analyzing signals, such as audio or sensor data.

💼 Career

Understanding window functions is important for jobs in audio engineering, communications, and data analysis involving time-series signals.

1

Create the signal vector

Create a variable called signal that is a row vector with these exact values: [1, 2, 3, 4, 5, 6, 7, 8]

MATLAB

% Create the signal vector called signal
% Your code here

Hint

Use square brackets [] to create a vector in MATLAB.

2

Create the Hamming window

Create a variable called window using the hamming function with the length of signal as input

MATLAB

signal = [1, 2, 3, 4, 5, 6, 7, 8];
% Create the Hamming window vector called window
% Your code here

Hint

Use length(signal) to get the number of elements in signal. Transpose the window to a row vector with '.

3

Apply the window to the signal

Create a variable called windowed_signal by multiplying signal and window element-wise

MATLAB

signal = [1, 2, 3, 4, 5, 6, 7, 8];
window = hamming(length(signal))';
% Multiply signal and window element-wise to create windowed_signal
% Your code here

Hint

Use the element-wise multiplication operator .* in MATLAB.

4

Display the original and windowed signals

Use disp to print signal and windowed_signal on separate lines

MATLAB

signal = [1, 2, 3, 4, 5, 6, 7, 8];
window = hamming(length(signal))';
windowed_signal = signal .* window;
% Display signal and windowed_signal
% Your code here

Hint

Use disp(variable) to print the value of a variable in MATLAB.

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