Convolution in MATLAB - Mini Project: Build & Apply

Convolution

📖 Scenario: Imagine you are working with simple signals in MATLAB. You want to combine two signals to see how one signal modifies the other. This process is called convolution and is very useful in signal processing, image processing, and many engineering fields.

🎯 Goal: You will write a MATLAB program that performs convolution of two given signals using the built-in conv function and display the result.

📋 What You'll Learn

Create two vectors representing signals with exact values

Create a variable to hold the length of the first signal

Use the conv function to convolve the two signals

Display the convolution result using disp

💡 Why This Matters

🌍 Real World

Convolution is used in audio processing to apply effects, in image processing to blur or sharpen images, and in engineering to analyze system responses.

💼 Career

Understanding convolution is important for careers in signal processing, communications, control systems, and data analysis.

1

Create the signals

Create two row vectors called signal1 and signal2 with these exact values: signal1 = [1 2 3] and signal2 = [4 5].

MATLAB

% Create the vectors signal1 and signal2 with the given values
% Your code here

Hint

Use square brackets [] to create row vectors in MATLAB.

2

Create a length variable

Create a variable called len1 that stores the length of signal1 using the length function.

MATLAB

signal1 = [1 2 3];
signal2 = [4 5];
% Create variable len1 to hold length of signal1
% Your code here

Hint

Use length(signal1) to get the number of elements in signal1.

3

Perform convolution

Create a variable called result that stores the convolution of signal1 and signal2 using the conv function.

MATLAB

signal1 = [1 2 3];
signal2 = [4 5];
len1 = length(signal1);
% Convolve signal1 and signal2 and store in result
% Your code here

Hint

Use conv(signal1, signal2) to get the convolution.

4

Display the result

Use disp to display the variable result.

MATLAB

signal1 = [1 2 3];
signal2 = [4 5];
len1 = length(signal1);
result = conv(signal1, signal2);
% Display the convolution result
% Your code here

Hint

Use disp(result) to print the convolution output.

Practice

1. What does the MATLAB function conv(x, h) compute?

easy

A. The convolution of vectors x and h

B. The element-wise multiplication of x and h

C. The dot product of x and h

D. The sum of vectors x and h

Solution

1. Step 1: Understand the function purpose

   The conv function in MATLAB is designed to compute the convolution of two vectors.

2. Step 2: Differentiate convolution from other operations

   Convolution combines two signals to produce a third, different from element-wise multiplication, dot product, or sum.

3. Final Answer:

   The convolution of vectors x and h -> Option A

4. Quick Check:

   conv(x, h) = convolution [OK]

Hint: Remember conv() means convolution, not multiplication [OK]

Common Mistakes:

• Confusing convolution with element-wise multiplication
• Thinking conv() sums vectors
• Mixing up dot product with convolution

2. Which of the following is the correct syntax to compute convolution of vectors a and b in MATLAB?

easy

A. conv(a, b)

B. convolve(a, b)

C. a * b

D. conv(a + b)

Solution

1. Step 1: Recall MATLAB convolution syntax

   MATLAB uses the function conv(x, h) to compute convolution of two vectors.

2. Step 2: Check each option

   conv(a, b) matches the correct syntax. convolve(a, b) is not a MATLAB function. a * b is matrix multiplication, not convolution. conv(a + b) has wrong argument format.

3. Final Answer:

   conv(a, b) -> Option A

4. Quick Check:

   Use conv(x, h) syntax [OK]

Hint: Use conv() with two arguments separated by comma [OK]

Common Mistakes:

• Using non-existent function convolve()
• Trying to multiply vectors with * for convolution
• Passing only one argument to conv()

3. What is the length of the output vector when you compute conv([1 2 3], [4 5]) in MATLAB?

medium

A. 6

B. 3

C. 5

D. 4

Solution

1. Step 1: Identify lengths of input vectors

   Vector [1 2 3] has length 3, and [4 5] has length 2.

2. Step 2: Calculate output length of convolution

   Output length = length(x) + length(h) - 1 = 3 + 2 - 1 = 4.

3. Final Answer:

   4 -> Option D

4. Quick Check:

   Output length = 3 + 2 - 1 = 4 [OK]

Hint: Output length = sum of input lengths minus one [OK]

Common Mistakes:

• Assuming output length equals input length
• Adding lengths without subtracting one
• Confusing convolution length with element-wise length

4. Consider the MATLAB code:

a = [1 2]; b = [3 4 5]; c = conv(a b);

What is the error in this code?

medium

A. Vectors a and b have different lengths

B. Missing comma between a and b in conv function

C. conv function does not exist in MATLAB

D. Using square brackets instead of parentheses

Solution

1. Step 1: Check syntax of conv function call

   The function call conv(a b) is missing a comma between the two input vectors.

2. Step 2: Verify other options

   Vectors can have different lengths for convolution. conv() is a valid MATLAB function. Square brackets are used correctly for vector definition, not in function call.

3. Final Answer:

   Missing comma between a and b in conv function -> Option B

4. Quick Check:

   Use comma to separate arguments in conv() [OK]

Hint: Separate arguments with comma inside conv() [OK]

Common Mistakes:

• Omitting comma between function arguments
• Thinking vectors must be same length
• Confusing vector definition brackets with function call syntax

5. You want to convolve two signals x = [1 0 2] and h = [3 4] but only keep the output length equal to the length of x. Which MATLAB command achieves this?

hard

A. conv(x, h, 'full')

B. conv(x, h)

C. conv(x, h, 'same')

D. conv(x, h, 'valid')

Solution

1. Step 1: Understand convolution output length options

   By default, conv(x, h) returns full convolution with length length(x)+length(h)-1.

2. Step 2: Use 'same' option to keep output length equal to x

   Using conv(x, h, 'same') returns the central part of the convolution, matching length of x.

3. Final Answer:

   conv(x, h, 'same') -> Option C

4. Quick Check:

   'same' option keeps output length equal to first input [OK]

Hint: Use 'same' option in conv() to match input length [OK]

Common Mistakes:

• Using default conv() which returns longer output
• Confusing 'valid' and 'same' options
• Expecting conv() to truncate output automatically