Filtering basics in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple moving average filter

What is the output of the following MATLAB code that applies a moving average filter to a signal?

MATLAB

x = [1 2 3 4 5];
windowSize = 3;
b = (1/windowSize)*ones(1,windowSize);
a = 1;
y = filter(b,a,x);
disp(y);

A [0.3333 1 2 3 4]

B [0 1 2 3 4]

C [1 2 3 4 5]

D [1 2 2 3 4]

💡 Hint

Think about how the filter function computes each output as a weighted sum of current and previous inputs.

The moving average filter with window size 3 uses b = [1/3 1/3 1/3], padding previous inputs with zeros. The first output is (1)/3 = 0.3333, the second (1 + 2)/3 = 1, the third (1 + 2 + 3)/3 = 2, and so on.

❓ Predict Output

intermediate

Effect of filter coefficients on output

What is the output of this MATLAB code that applies a filter with coefficients b and a to the input vector x?

MATLAB

x = [0 1 0 0 0];
b = [1 1];
a = 1;
y = filter(b,a,x);
disp(y);

A [0 1 1 0 0]

B [1 1 0 0 0]

C [0 1 0 0 0]

D [1 0 0 0 0]

💡 Hint

The filter output at each step depends on current and previous inputs weighted by b coefficients.

The filter output y[n] = b(1)*x[n] + b(2)*x[n-1]. For input x = [0 1 0 0 0], y = [0, 1, 1, 0, 0].

🔧 Debug

advanced

Identify the error in filter usage

What error does this MATLAB code produce when run?

MATLAB

x = [1 2 3 4];
b = [1 2 3];
a = [1 0];
y = filter(b,a,x);

A Error: 'a' must be a scalar or vector with length equal to or less than 'b'

B Error: Inputs must be vectors of the same length

C No error, outputs filtered vector

D Error: Filter denominator coefficients 'a' cannot have zeros except the first element

💡 Hint

Check the denominator coefficients 'a' for invalid values.

No error is produced. MATLAB's filter function requires only that a(1) ~= 0; zeros in other positions of 'a' are allowed and the code runs successfully, producing a filtered vector.

🧠 Conceptual

advanced

Understanding filter initial conditions

What is the effect of specifying initial conditions in the MATLAB filter function?

A It changes the filter coefficients permanently

B It sets the starting state of the filter to avoid transient effects

C It resets the input vector to zeros before filtering

D It has no effect on the filter output

💡 Hint

Think about how filters remember past inputs or outputs.

Initial conditions set the filter's internal state at the start, which helps avoid transient effects caused by assuming zero past inputs or outputs.

❓ Predict Output

expert

Output length after filtering with different coefficient lengths

What is the length of the output vector y after running this MATLAB code?

MATLAB

x = 1:5;
b = [1 -1 1];
a = 1;
y = filter(b,a,x);

A 7

B 6

C 3

D 5

💡 Hint

The filter function output length matches the input length.

The filter function returns an output vector y with the same length as the input vector x, regardless of the length of coefficients b and a.

Practice

1. What does filtering an array in MATLAB mean?
filtered = array(condition);

easy

A. Selecting elements that meet a condition

B. Sorting the array elements

C. Changing the array size randomly

D. Adding new elements to the array

Solution

1. Step 1: Understand filtering concept

   Filtering means choosing only those elements from an array that satisfy a condition.

2. Step 2: Analyze the MATLAB syntax

   The syntax array(condition) returns elements where the condition is true.

3. Final Answer:

   Selecting elements that meet a condition -> Option A

4. Quick Check:

   Filtering = Selecting elements [OK]

Hint: Filtering picks elements matching condition inside parentheses [OK]

Common Mistakes:

• Thinking filtering sorts the array
• Believing filtering changes array size randomly
• Confusing filtering with adding elements

2. Which of the following is the correct MATLAB syntax to filter array A for values greater than 10?

easy

A. filtered = A > 10;

B. filtered = A{A > 10};

C. filtered = A(A > 10);

D. filtered = filter(A > 10);

Solution

1. Step 1: Identify correct filtering syntax

   In MATLAB, filtering uses parentheses with a logical condition inside to select elements.

2. Step 2: Check each option

   filtered = A(A > 10); uses A(A > 10), which correctly filters elements greater than 10.

3. Final Answer:

   filtered = A(A > 10); -> Option C

4. Quick Check:

   Use parentheses with condition for filtering [OK]

Hint: Use parentheses with condition to filter arrays [OK]

Common Mistakes:

• Using > without parentheses returns logical array, not filtered values
• Using curly braces {} which are for cell arrays
• Using undefined function 'filter'

3. What is the output of this MATLAB code?

A = [3, 12, 7, 15, 9];
filtered = A(A >= 10);
disp(filtered);

medium

A. Error

B. [3 7 9]

C. [3 12 7 15 9]

D. [12 15]

Solution

1. Step 1: Understand filtering condition

   The condition A >= 10 selects elements in A that are 10 or greater.

2. Step 2: Apply condition to array A

   Elements 12 and 15 satisfy this condition, so filtered = [12 15].

3. Final Answer:

   [12 15] -> Option D

4. Quick Check:

   Elements >= 10 = [12 15] [OK]

Hint: Filter keeps elements where condition is true [OK]

Common Mistakes:

• Including elements less than 10
• Expecting original array output
• Confusing logical array with filtered values

4. Identify the error in this MATLAB code for filtering values less than 5:

A = [2, 8, 4, 6];
filtered = A{A < 5};

medium

A. Using curly braces {} instead of parentheses ()

B. Missing semicolon at end of line

C. Incorrect comparison operator

D. Array A is not defined

Solution

1. Step 1: Check filtering syntax

   Filtering arrays uses parentheses (), not curly braces {} which are for cell arrays.

2. Step 2: Identify the error

   Using A{A < 5} causes an error because curly braces cannot index numeric arrays.

3. Final Answer:

   Using curly braces {} instead of parentheses () -> Option A

4. Quick Check:

   Use () for filtering numeric arrays [OK]

Hint: Use parentheses () to filter numeric arrays, not curly braces {} [OK]

Common Mistakes:

• Using {} for numeric array indexing
• Ignoring MATLAB error messages
• Confusing semicolon necessity

5. Given a matrix M = [1 5 9; 4 2 7; 8 3 6], how do you filter all elements greater than 4 and return them as a single column vector?

hard

A. filtered = filter(M > 4);

B. filtered = M(M > 4); filtered = filtered(:);

C. filtered = M{M > 4};

D. filtered = M(:, M > 4);

Solution

1. Step 1: Apply filtering condition

   Use M(M > 4) to select all elements greater than 4 from matrix M.

2. Step 2: Convert result to column vector

   Use filtered(:) to reshape the filtered elements into a single column vector.

3. Final Answer:

   filtered = M(M > 4); filtered = filtered(:); -> Option B

4. Quick Check:

   Filter then reshape to column vector [OK]

Hint: Filter with condition, then reshape using (: ) for column vector [OK]

Common Mistakes:

• Using curly braces {} for filtering
• Trying to filter columns instead of elements
• Using undefined function 'filter'