Zero-order hold in Simulink - Time & Space Complexity

Time Complexity: Zero-order hold

O(n)

Understanding Time Complexity

We want to understand how the time needed to run a zero-order hold block changes as the input size grows.

How does the block's processing time grow when the input signal length increases?

Scenario Under Consideration

Analyze the time complexity of the following Simulink zero-order hold block behavior.

% Zero-order hold block behavior in Simulink
last_sample_index = 1;
for k = 1 : length(input_signal)
    output_signal(k) = input_signal(last_sample_index);
    if mod(k, sample_time) == 0
        last_sample_index = k;
    end
end

This code holds the last sampled input value constant until the next sample time, producing the output signal.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each element of the input signal to assign output values.
• How many times: Once for every element in the input signal (n times).

How Execution Grows With Input

As the input signal length grows, the number of operations grows directly with it.

Input Size (n)	Approx. Operations
10	10
100	100
1000	1000

Pattern observation: The operations increase in a straight line as input size increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to process grows directly in proportion to the input size.

Common Mistake

[X] Wrong: "The zero-order hold processes all samples instantly regardless of input size."

[OK] Correct: Even though it holds values constant, it still needs to process each input element once, so time grows with input length.

Interview Connect

Understanding how simple blocks like zero-order hold scale helps you reason about system performance and efficiency in real projects.

Self-Check

"What if the zero-order hold sampled at twice the rate? How would the time complexity change?"

Practice

1.

What is the main function of a Zero-order hold block in Simulink?

easy

A. It converts continuous signals to discrete signals.

B. It differentiates the input signal continuously.

C. It integrates the input signal over time.

D. It holds the input value constant between sample times.

Solution

1. Step 1: Understand the role of Zero-order hold and compare options

   The Zero-order hold block keeps the input value constant during the sample period. It does not differentiate, integrate, or convert continuous to discrete signals.

2. Final Answer:

   It holds the input value constant between sample times. -> Option D

3. Quick Check:

   Zero-order hold = hold input constant [OK]

Hint: Remember: zero-order hold means 'hold value constant' [OK]

Common Mistakes:

• Confusing zero-order hold with differentiation or integration
• Thinking it converts continuous to discrete signals
• Assuming it changes the signal value continuously

2.

Which of the following is the correct way to set the fixed sample time parameter in a Zero-order hold block in Simulink?

easy

A. Set sample time to a positive number like 0.1 seconds.

B. Set sample time to -1 for inherited sample time.

C. Set sample time to 0 for continuous operation.

D. Set sample time to a negative number other than -1.

Solution

1. Step 1: Understand sample time settings and evaluate options

   Fixed sample time must be a positive number (e.g., 0.1s) to specify hold duration. -1 inherits from input; 0 means continuous (no hold); other negatives invalid.

2. Final Answer:

   Set sample time to a positive number like 0.1 seconds. -> Option A

3. Quick Check:

   Sample time positive number = correct setting [OK]

Hint: Sample time must be positive for zero-order hold [OK]

Common Mistakes:

• Using zero or negative sample times incorrectly
• Confusing inherited sample time (-1) with explicit sample time
• Setting sample time to continuous (0) for discrete hold

3.

Consider this Simulink model snippet using a Zero-order hold block with sample time 0.5 seconds. The input signal is a step that changes from 0 to 1 at time 0.3 seconds. What will be the output of the Zero-order hold block at time 0.7 seconds?

medium

A. 0.5

B. 0

C. 1

D. Undefined

Solution

1. Step 1: Analyze sample intervals and input timing

   With sample time 0.5s, samples at 0, 0.5, 1.0s. Step changes at 0.3s, so input(0)=0, input(0.5)=1. At 0.7s (in [0.5,1.0)), holds 1.

2. Final Answer:

   1 -> Option C

3. Quick Check:

   Output holds last sampled input = 1 [OK]

Hint: Output holds input at last sample time before current time [OK]

Common Mistakes:

• Thinking sample at 0.5s captures 0 despite change at 0.3s
• Ignoring sample time intervals
• Confusing step change time with sample time

4.

In a Simulink model, a Zero-order hold block is set with sample time 0.2 seconds. The output signal is not holding values as expected and changes continuously. What is the most likely cause?

medium

A. Sample time is set to 0 (continuous) instead of 0.2.

B. Input signal is discrete, so hold is unnecessary.

C. Zero-order hold block is connected incorrectly.

D. Sample time is set to a negative number other than -1.

Solution

1. Step 1: Identify cause of continuous output behavior

   If sample time=0, block operates continuously (follows input without holding). Other causes less likely to produce continuous change.

2. Final Answer:

   Sample time is set to 0 (continuous) instead of 0.2. -> Option A

3. Quick Check:

   Continuous sample time = no hold [OK]

Hint: Check sample time is positive, not zero [OK]

Common Mistakes:

• Ignoring sample time setting
• Assuming input signal type causes issue
• Misconnecting blocks without checking parameters

5.

You want to convert a discrete sensor signal sampled every 0.1 seconds into a continuous signal for further processing in Simulink. Which approach using a Zero-order hold block is correct?

Choose the best option.

hard

A. Do not use Zero-order hold; use a continuous integrator instead.

B. Set the Zero-order hold sample time to 0.1 seconds to hold each sample value constant until the next sample.

C. Set the Zero-order hold sample time to -1 to inherit sample time from input.

D. Set the Zero-order hold sample time to 0 to make the output continuous.

Solution

1. Step 1: Understand goal and evaluate ZOH configurations

   Goal: hold discrete samples constant between 0.1s intervals for continuous output. Set Ts=0.1s matches sensor rate. Ts=0 continuous (no hold); -1 inherits (risk mismatch); integrator changes values.

2. Final Answer:

   Set the Zero-order hold sample time to 0.1 seconds to hold each sample value constant until the next sample. -> Option B

3. Quick Check:

   Sample time = sensor rate for correct hold [OK]

Hint: Match hold sample time to sensor sample interval [OK]

Common Mistakes:

• Setting sample time to zero for hold
• Using inherited sample time without checking input
• Replacing hold with integrator incorrectly