Filtering basics in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of filtering in signal processing?

Filtering is used to remove unwanted parts of a signal, such as noise, or to extract useful parts like specific frequency components.

beginner

What is the difference between a low-pass and a high-pass filter?

A low-pass filter lets low frequencies pass and blocks high frequencies. A high-pass filter lets high frequencies pass and blocks low frequencies.

intermediate

In MATLAB, which function is commonly used to apply a simple moving average filter?

The function filter can be used with appropriate coefficients to apply a moving average filter.

intermediate

What does the MATLAB command y = filter(b, a, x); do?

It applies a digital filter defined by numerator coefficients b and denominator coefficients a to the input signal x, producing the filtered output y.

advanced

Why is it important to understand the filter coefficients b and a in MATLAB filtering?

Because b and a define the filter's behavior: b controls the zeros (numerator) and a controls the poles (denominator), which together shape the frequency response.

Which MATLAB function is used to apply a digital filter to a signal?

A filter

B fft

C plot

D conv

The filter function applies a digital filter to a signal using given coefficients.

What type of filter would you use to remove high-frequency noise from a signal?

A High-pass filter

B Low-pass filter

C Band-stop filter

D All-pass filter

A low-pass filter removes high-frequency components, which is useful to reduce high-frequency noise.

In the command y = filter(b, a, x);, what does x represent?

A Frequency response

B Filter coefficients

C Output signal

D Input signal

x is the input signal to be filtered.

Which of these is NOT a typical goal of filtering?

A Feature extraction

B Noise reduction

C Signal amplification

D Frequency selection

Filtering usually modifies frequency content but does not amplify signals; amplification is done by other processes.

What does a moving average filter do?

A Smooths the signal by averaging nearby points

B Amplifies high frequencies

C Removes DC offset

D Converts signal to frequency domain

A moving average filter smooths a signal by averaging adjacent samples to reduce noise.

Explain how you would use MATLAB to remove noise from a signal using filtering.

Think about choosing filter coefficients and applying the filter function.

Describe the difference between low-pass and high-pass filters and give an example of when to use each.

Consider what parts of the signal you want to keep or remove.

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'