Unit delay block in Simulink - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the Unit Delay Block Behavior

In Simulink, what does the Unit Delay block do to the input signal?

A It outputs the input signal delayed by one simulation time step.

B It outputs the input signal immediately without any delay.

C It outputs the input signal delayed by two simulation time steps.

D It outputs the input signal advanced by one simulation time step.

💡 Hint

Think about how the block stores and outputs the previous input value.

The Unit Delay block outputs the input value from the previous simulation step, effectively delaying the signal by one time step.

❓ Predict Output

intermediate

Output of Unit Delay Block with Step Input

Given a step input signal starting at 0 and switching to 1 at time step 3, what is the output of a Unit Delay block at time step 4?

Simulink

Time steps: 0,1,2,3,4
Input:     0,0,0,1,1
Unit Delay output at time t = input at time t-1

A 0

B Undefined

C 1

D 2

💡 Hint

Remember the output at time t is the input at time t-1.

At time 4, the output is the input at time 3, which is 1.

❓ data_output

advanced

Simulate Unit Delay Output Sequence

Given the input sequence [2, 4, 6, 8, 10] to a Unit Delay block with initial condition 0, what is the output sequence?

Simulink

Input sequence: [2, 4, 6, 8, 10]
Initial condition: 0
Output at time t = input at time t-1 (or initial condition at t=0)

A [2, 4, 6, 8, 10]

B [0, 2, 4, 6, 8]

C [2, 2, 4, 6, 8]

D [0, 0, 2, 4, 6]

💡 Hint

The first output is the initial condition, then outputs previous inputs.

The output starts with the initial condition 0, then outputs each previous input value shifted by one step.

🔧 Debug

advanced

Identify the Error in Unit Delay Block Setup

A user sets the initial condition of a Unit Delay block to a string value 'zero'. What error will Simulink produce when running the model?

A Simulation runs but output is always zero regardless of input.

B No error; Simulink converts string to zero automatically.

C Type mismatch error because initial condition must be numeric.

D Syntax error in the model configuration.

💡 Hint

Consider the data type requirements for initial conditions.

The initial condition must be numeric. Using a string causes a type mismatch error.

🚀 Application

expert

Using Unit Delay for Recursive Computation

You want to compute the Fibonacci sequence in Simulink using Unit Delay blocks. Which setup correctly uses Unit Delay blocks to output the next Fibonacci number at each time step?

A Use one Unit Delay block initialized to 1 and feed its output back to its input directly.

B Use two Unit Delay blocks in parallel, both initialized to 1, and multiply their outputs to get the next number.

C Use one Unit Delay block initialized to 0 and add a constant 1 at each step.

D Use two Unit Delay blocks in series, each initialized to 0 and 1, then sum their outputs to get the next number.

💡 Hint

Recall Fibonacci numbers are sums of the two previous numbers.

Two Unit Delay blocks store the two previous Fibonacci numbers. Summing their outputs produces the next number.

Practice

1. What does the Unit Delay block in Simulink do?

easy

A. Outputs the previous input value, delaying the signal by one step

B. Outputs the current input value without delay

C. Outputs the sum of all past inputs

D. Outputs a random value at each step

Solution

1. Step 1: Understand the function of Unit Delay block

   The Unit Delay block holds the input value and outputs it one time step later, effectively delaying the signal by one step.

2. Step 2: Compare options with the definition

   Only Outputs the previous input value, delaying the signal by one step correctly describes this behavior; others describe different or incorrect behaviors.

3. Final Answer:

   Outputs the previous input value, delaying the signal by one step -> Option A

4. Quick Check:

   Unit Delay = previous input output [OK]

Hint: Remember: Unit Delay outputs last step's input [OK]

Common Mistakes:

• Thinking it outputs current input immediately
• Confusing with blocks that sum inputs
• Assuming it outputs random or initial values only

2. Which of the following is the correct way to set the initial condition of a Unit Delay block in Simulink?

easy

A. Initialize the input signal to zero externally

B. Use a separate Gain block before the Unit Delay

C. Set the 'Initial condition' parameter in the block's dialog box

D. Set the initial condition in the MATLAB workspace only

Solution

1. Step 1: Identify how initial conditions are set in Unit Delay

   The Unit Delay block has a parameter called 'Initial condition' in its dialog box where you specify the output value at the first time step.

2. Step 2: Evaluate the options

   Set the 'Initial condition' parameter in the block's dialog box correctly states this method. Options B, C, and D describe indirect or incorrect ways.

3. Final Answer:

   Set the 'Initial condition' parameter in the block's dialog box -> Option C

4. Quick Check:

   Initial condition set inside block dialog [OK]

Hint: Set initial condition inside Unit Delay block dialog [OK]

Common Mistakes:

• Trying to set initial condition outside the block
• Using other blocks to simulate initial condition
• Assuming MATLAB workspace variable sets it automatically

3. Consider a Unit Delay block with initial condition 0. The input signal over 4 time steps is [1, 3, 5, 7]. What is the output sequence?

medium

A. [1, 3, 5, 7]

B. [0, 1, 3, 5]

C. [1, 1, 3, 5]

D. [0, 0, 1, 3]

Solution

1. Step 1: Understand Unit Delay output behavior

   At each time step, output is the input from the previous step. At step 1, output is initial condition (0).

2. Step 2: Calculate output for each step

   Step 1 output: 0 (initial condition)
   Step 2 output: input at step 1 = 1
   Step 3 output: input at step 2 = 3
   Step 4 output: input at step 3 = 5

3. Final Answer:

   [0, 1, 3, 5] -> Option B

4. Quick Check:

   Output lags input by one step [OK]

Hint: Output is previous input; first output = initial condition [OK]

Common Mistakes:

• Outputting current input instead of previous
• Forgetting initial condition at first step
• Shifting output incorrectly by more than one step

4. You have a Unit Delay block with initial condition 5, but the output starts at 0 instead. What is the likely cause?

medium

A. The initial condition parameter was not set correctly in the block

B. The input signal is zero at the first step

C. The Unit Delay block is connected incorrectly

D. Simulink does not support initial conditions in Unit Delay blocks

Solution

1. Step 1: Analyze the initial condition effect

   The Unit Delay block outputs the initial condition at the first step if set properly.

2. Step 2: Identify why output is zero instead of 5

   If output is zero, likely the initial condition parameter was not set or saved correctly in the block dialog.

3. Final Answer:

   The initial condition parameter was not set correctly in the block -> Option A

4. Quick Check:

   Initial condition must be set inside block [OK]

Hint: Check initial condition parameter inside block dialog [OK]

Common Mistakes:

• Assuming input signal affects initial output
• Thinking connection errors cause initial output zero
• Believing Simulink ignores initial conditions

5. You want to model a system where the output at each step is the sum of the current input and the previous input. How can you use a Unit Delay block to achieve this?

hard

A. Set the initial condition of the Unit Delay block to the sum of inputs

B. Use two Unit Delay blocks in series and sum their outputs

C. Use a Unit Delay block with initial condition zero and multiply by input

D. Add the current input to the output of a Unit Delay block that delays the input by one step

Solution

1. Step 1: Understand the requirement

   The output should be current input plus previous input value.

2. Step 2: Use Unit Delay to get previous input

   A Unit Delay block outputs the previous input. Adding this output to the current input gives the desired sum.

3. Step 3: Evaluate options

   Add the current input to the output of a Unit Delay block that delays the input by one step correctly describes this setup. Options A, B, and D do not produce the required output.

4. Final Answer:

   Add the current input to the output of a Unit Delay block that delays the input by one step -> Option D

5. Quick Check:

   Sum = current input + delayed input [OK]

Hint: Sum current input with Unit Delay output for previous input [OK]

Common Mistakes:

• Using multiple Unit Delay blocks unnecessarily
• Misusing initial condition to store sums
• Multiplying instead of adding signals