Signal routing in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this signal routing code?

Consider the following MATLAB code that routes signals through a switch matrix. What will be the value of outputSignal after execution?

MATLAB

inputSignal = [1 2 3 4];
switchMatrix = [0 1 0 0; 1 0 0 0; 0 0 0 1; 0 0 1 0];
routeIndex = 2;
outputSignal = inputSignal * switchMatrix(routeIndex, :)';

A 1

B 2

C [2]

D 1 0 0 0

💡 Hint

Remember that MATLAB matrix multiplication rules apply and the switchMatrix row selects which inputSignal elements are routed.

The code multiplies the inputSignal vector by the second row of switchMatrix transposed. The second row is [1 0 0 0], so the multiplication sums inputSignal elements weighted by this row: 1*1 + 2*0 + 3*0 + 4*0 = 1. But since inputSignal is a row vector and switchMatrix(row,:) is a row vector, the multiplication inputSignal * switchMatrix(routeIndex, :)' results in a scalar equal to 1.

🧠 Conceptual

intermediate

Which statement correctly describes signal routing in MATLAB?

In MATLAB, when routing signals using matrices, which of the following statements is true?

A Signal routing is achieved by multiplying the input signal vector by a routing matrix that acts as a selector.

B Signal routing can be done by element-wise multiplication of input and routing matrices.

C Signal routing requires loops to assign each input to output manually.

D Signal routing is only possible using Simulink, not MATLAB code.

💡 Hint

Think about how matrix multiplication can select and combine signals.

In MATLAB, signal routing can be efficiently done by multiplying an input signal vector by a routing matrix. The routing matrix acts as a selector or switch, directing inputs to outputs by matrix multiplication.

🔧 Debug

advanced

Identify the error in this signal routing code

The following MATLAB code is intended to route signals from inputSignal to outputSignal using routingMatrix. What error will occur when running this code?

MATLAB

inputSignal = [1 2 3];
routingMatrix = [0 1 0; 1 0 0];
outputSignal = inputSignal * routingMatrix;

A No error; outputSignal will be [2 1 0].

B Dimension mismatch error due to incompatible matrix sizes for multiplication.

C Runtime error because routingMatrix contains zeros.

D Syntax error due to missing semicolon.

💡 Hint

Check the sizes of the matrices involved in multiplication.

inputSignal is a 1x3 vector, routingMatrix is 2x3. Multiplying 1x3 by 2x3 is invalid because inner dimensions must match (3 and 2 do not). This causes a dimension mismatch error.

❓ Predict Output

advanced

What is the output of this complex routing example?

Given the following MATLAB code, what is the value of outputSignal?

MATLAB

inputSignal = [10 20 30 40];
routingMatrix = [1 0 0 0; 0 0 1 0; 0 1 0 0; 0 0 0 1];
outputSignal = routingMatrix * inputSignal';

A [40; 20; 30; 10]

B [10 30 20 40]

C [10; 30; 20; 40]

D [10; 20; 30; 40]

💡 Hint

Remember that inputSignal is a row vector and is transposed to a column vector before multiplication.

routingMatrix is 4x4 and inputSignal' is 4x1. Multiplying routingMatrix by inputSignal' results in a 4x1 vector. The routingMatrix rearranges the inputSignal elements: first row picks element 1 (10), second row picks element 3 (30), third row picks element 2 (20), fourth row picks element 4 (40).

🚀 Application

expert

How many output signals are produced by this routing matrix?

Given the routing matrix below, how many output signals will be generated when routing an input vector of length 5?

MATLAB

routingMatrix = [1 0 0 0 0;
                 0 1 0 0 0;
                 0 0 1 0 0;
                 0 0 0 1 0];

A 0

B 5

C 1

D 4

💡 Hint

The number of output signals corresponds to the number of rows in the routing matrix.

The routing matrix has 4 rows and 5 columns. When multiplying by an input vector of length 5, the output vector length equals the number of rows, which is 4.

Practice

1. What is the main purpose of signal routing in MATLAB programming?

easy

A. To send data to different parts of a program based on conditions

B. To create graphical user interfaces

C. To perform mathematical calculations only

D. To store data permanently on disk

Solution

1. Step 1: Understand signal routing concept

   Signal routing means directing data flow to different parts depending on conditions.

2. Step 2: Match purpose with options

   Only To send data to different parts of a program based on conditions describes sending data based on conditions, which is signal routing.

3. Final Answer:

   To send data to different parts of a program based on conditions -> Option A

4. Quick Check:

   Signal routing = conditional data flow [OK]

Hint: Signal routing controls data flow based on conditions [OK]

Common Mistakes:

• Confusing signal routing with data storage
• Thinking it only does calculations
• Mixing it up with GUI creation

2. Which of the following is the correct syntax to route a signal based on a condition in MATLAB?

easy

A. if signal > 0 {
output = signal;
} else {
output = 0;
}

B. if (signal > 0) then
output = signal
else
output = 0
end if

C. if signal > 0
output = signal;
else
output = 0;
end

D. if signal > 0:
output = signal
else:
output = 0

Solution

1. Step 1: Recall MATLAB if-else syntax

   MATLAB uses 'if condition', statements, 'else', statements, and 'end' to close.

2. Step 2: Compare options with MATLAB syntax

   if signal > 0 output = signal; else output = 0; end matches MATLAB syntax exactly; others use syntax from other languages.

3. Final Answer:

   if signal > 0 output = signal; else output = 0; end -> Option C

4. Quick Check:

   MATLAB if-else ends with 'end' [OK]

Hint: MATLAB if-else blocks end with 'end' keyword [OK]

Common Mistakes:

• Using 'then' keyword (not in MATLAB)
• Using braces {} instead of end
• Using colons like Python

3. What will be the output of this MATLAB code?

signal = -5;
if signal > 0
    routed = 1;
else
    routed = -1;
end
routed

medium

A. -1

B. 1

C. 0

D. Error

Solution

1. Step 1: Check the condition signal > 0

   signal is -5, which is not greater than 0, so condition is false.

2. Step 2: Follow else branch

   Since condition is false, routed is assigned -1.

3. Final Answer:

   -1 -> Option A

4. Quick Check:

   signal = -5 -> routed = -1 [OK]

Hint: Check condition truth to pick if or else branch [OK]

Common Mistakes:

• Assuming negative numbers satisfy > 0
• Confusing output variable name
• Expecting zero output

4. Identify the error in this MATLAB signal routing code:

signal = 10;
if signal > 5
    output = 1;
else
    output = 0;

medium

A. Variable 'output' is not defined

B. Missing 'end' to close the if statement

C. Incorrect comparison operator

D. Using semicolons incorrectly

Solution

1. Step 1: Check if statement structure

   MATLAB requires 'end' to close if blocks.

2. Step 2: Verify code completeness

   The code lacks 'end' after else block, causing syntax error.

3. Final Answer:

   Missing 'end' to close the if statement -> Option B

4. Quick Check:

   if blocks must end with 'end' [OK]

Hint: Always close if with 'end' in MATLAB [OK]

Common Mistakes:

• Forgetting 'end' after if-else
• Thinking semicolons end blocks
• Misusing comparison operators

5. You want to route a signal in MATLAB to three different outputs based on its value:
- If signal < 0, output = -1
- If signal == 0, output = 0
- If signal > 0, output = 1
Which code correctly implements this routing?

hard

A. if signal < 0
output = -1;
else if signal == 0
output = 0;
else
output = 1;
end

B. if signal <= 0
output = -1;
elseif signal == 0
output = 0;
else
output = 1;
end

C. if signal < 0
output = -1;
if signal == 0
output = 0;
else
output = 1;
end

D. if signal < 0
output = -1;
elseif signal == 0
output = 0;
else
output = 1;
end

Solution

1. Step 1: Understand routing conditions

   We need three cases: less than 0, equal to 0, greater than 0.

2. Step 2: Check code correctness

   if signal < 0 output = -1; elseif signal == 0 output = 0; else output = 1; end uses if, elseif, else correctly with proper conditions and 'end'.

3. Step 3: Identify errors in other options

   if signal <= 0 output = -1; elseif signal == 0 output = 0; else output = 1; end wrongly uses <= which overlaps conditions; C uses two separate ifs causing logic errors; D uses 'else if' which is invalid syntax in MATLAB.

4. Final Answer:

   if signal < 0 output = -1; elseif signal == 0 output = 0; else output = 1; end -> Option D

5. Quick Check:

   Use if-elseif-else for multiple conditions [OK]

Hint: Use if-elseif-else for multiple exclusive conditions [OK]

Common Mistakes:

• Using overlapping conditions like <= and ==
• Using nested if without else properly
• Writing 'else if' instead of 'elseif'