Unit delay block in Simulink - Step-by-Step Execution

Concept Flow - Unit delay block

Input Signal at time t

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Unit Delay Block

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Output Signal at time t

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Store current input as next output

↩Back to Output Signal at time t+1

The unit delay block outputs the previous input value, delaying the signal by one time step.

Execution Sample

Simulink

Input: [1, 2, 3, 4]
Output: [0, 1, 2, 3]
Initial output = 0

This shows how the unit delay block outputs the previous input value, starting with an initial output of 0.

Execution Table

Step	Input at t	Output at t	Stored for next output
1	1	0 (initial)	1
2	2	1	2
3	3	2	3
4	4	3	4
5	-	4	-

💡 Input sequence ends; output at step 5 is last stored input.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	Final
Input at t	-	1	2	3	4	-
Output at t	0	0	1	2	3	4
Stored value	-	1	2	3	4	4

Key Moments - 2 Insights

Why is the output at step 1 zero and not the input value 1?

Because the unit delay block outputs the previous input value. At step 1, there is no previous input, so it outputs the initial value 0 as shown in execution_table row 1.

How does the stored value relate to the output at the next step?

The stored value at the current step becomes the output at the next step. For example, stored value 1 at step 1 is output at step 2 (execution_table rows 1 and 2).

Visual Quiz - 3 Questions

Look at the execution table, what is the output at step 3?

A 2

B 3

C 1

D 0

💡 Hint

Check the 'Output at t' column in execution_table row 3.

At which step does the output first equal the input value 2?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at when output matches input 2 in execution_table rows.

If the initial output was set to 5 instead of 0, what would be the output at step 1?

A 0

B 5

C 1

D Undefined

💡 Hint

Initial output value is used at step 1 as shown in execution_table row 1.

Concept Snapshot

Unit delay block outputs the previous input value.
Initial output is set before inputs start.
At time t, output = input at time t-1.
Delays signal by one time step.
Used to model memory or feedback in systems.

Full Transcript

The unit delay block in Simulink delays the input signal by one time step. It outputs the previous input value at each time step. Initially, it outputs a preset initial value, often zero. For example, if the input sequence is 1, 2, 3, 4, the output sequence will be 0, 1, 2, 3. The block stores the current input to output it in the next step. This behavior is useful to model systems with memory or feedback loops.

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