Convolution in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is convolution in signal processing?

Convolution is a mathematical way to combine two signals to see how one modifies or shapes the other. It helps us understand how a system responds to an input.

beginner

What MATLAB function is used to perform convolution of two vectors?

The MATLAB function conv() is used to calculate the convolution of two vectors or signals.

intermediate

Explain the size of the output vector when convolving two vectors of lengths M and N.

The output vector length after convolution is M + N - 1. This happens because convolution combines every element of the first vector with every element of the second.

intermediate

What does the convolution operation represent in terms of system behavior?

Convolution represents how an input signal is modified by a system's impulse response, showing the output signal of the system.

beginner

Write a simple MATLAB code snippet to convolve two vectors a = [1 2 3] and b = [4 5].

a = [1 2 3]; b = [4 5]; c = conv(a, b); disp(c); This will output: [4 13 22 15]

What MATLAB function do you use to perform convolution?

A conv()

B filter()

C fft()

D sum()

The conv() function is specifically designed for convolution in MATLAB.

If vector A has length 3 and vector B has length 4, what is the length of their convolution result?

A 3

B 12

C 4

D 6

The length is 3 + 4 - 1 = 6.

What does convolution help us find in signal processing?

A The difference between two signals

B The sum of two signals

C How one signal modifies another

D The maximum value of a signal

Convolution shows how one signal changes or shapes another.

Which of these is NOT true about convolution?

A It combines two signals

B It always produces a shorter output

C It can represent system output

D It uses the impulse response

Convolution output is usually longer, not shorter.

In MATLAB, what does conv([1 2], [3 4]) return?

A [3 10 8]

B [3 7 8]

C [4 10 8]

D [1 2 3 4]

The convolution is calculated as [1*3, 1*4+2*3, 2*4] = [3 10 8].

Explain in your own words what convolution means and why it is useful in signal processing.

Think about how one signal changes another.

Describe how to use MATLAB to perform convolution on two vectors and what the output represents.

Focus on the MATLAB function and the meaning of the result.

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