Convolution in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the convolution of vectors x and h.

MATLAB

y = conv(x, [1]);

Drag options to blanks, or click blank then click option'

Ah

Bx

Csum

Dprod

Attempts:

3 left

💡 Hint

Common Mistakes

Using x as both inputs to conv.

Using functions like sum or prod instead of a vector.

The conv function in MATLAB computes the convolution of two vectors. Here, h is the second vector to convolve with x.

2fill in blank

medium

Complete the code to create a vector h of length 3 with all ones for convolution.

MATLAB

h = [1](1, 3);

Drag options to blanks, or click blank then click option'

Aeye

Bzeros

Crand

Dones

Attempts:

3 left

💡 Hint

Common Mistakes

Using zeros which creates zeros instead of ones.

Using eye which creates an identity matrix.

The ones function creates a vector of ones. Here, ones(1,3) creates a row vector with three ones.

3fill in blank

hard

Fix the error in the convolution code by completing the blank.

MATLAB

y = conv(x, h, [1]);

Drag options to blanks, or click blank then click option'

A'full'

B'same'

C'none'

D'valid'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'none' which is not a valid option.

Using 'valid' which returns a smaller output.

The third argument in conv specifies the size of the output. 'same' returns the central part of the convolution that is the same size as x.

4fill in blank

hard

Fill all three blanks to create a convolution vector h with values 1, 2, 3 and compute convolution with x.

MATLAB

h = [[1], [2], [3]];
y = conv(x, h);

Drag options to blanks, or click blank then click option'

A1

B2

C3

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Using values outside the requested range.

Not using commas to separate values.

The vector h should contain the values 1, 2, 3.

5fill in blank

hard

Fill all four blanks to create a vector h with values 1, 2, 3 and compute convolution with x using 'same' output size.

MATLAB

h = [[1], [2], [3]];
y = conv(x, h, [4]);

Drag options to blanks, or click blank then click option'

A1

B2

C3

D'same'

Attempts:

3 left

💡 Hint

Common Mistakes

Using numbers instead of the string 'same' for the conv argument.

Missing commas between vector elements.

The vector h is defined with values 1, 2, and 3. The convolution uses the 'same' option to keep the output size equal to x.

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