PWM generation in Simulink - Time & Space Complexity

Time Complexity: PWM generation in Simulink

O(N)

Understanding Time Complexity

We want to understand how the time needed to generate PWM signals changes as the input size changes.

Specifically, how does the system behave when the number of PWM channels or signal resolution increases?

Scenario Under Consideration

Analyze the time complexity of the following PWM generation setup in Simulink.

% Simulink model snippet for PWM generation
% 1. Compare input signal with carrier waveform
% 2. Generate PWM output based on comparison
% 3. Repeat for each PWM channel

for i = 1:N_channels
  pwm_output(i) = input_signal(i) > carrier_waveform;
end
    

This code compares each input signal with a carrier waveform to create PWM signals for multiple channels.

Identify Repeating Operations

Look at what repeats in this process.

• Primary operation: Comparing input signals to the carrier waveform.
• How many times: Once for each PWM channel, so N times.

How Execution Grows With Input

As the number of PWM channels increases, the number of comparisons grows directly with it.

Input Size (N_channels)	Approx. Operations
10	10 comparisons
100	100 comparisons
1000	1000 comparisons

Pattern observation: The operations increase in a straight line as channels increase.

Final Time Complexity

Time Complexity: O(N)

This means the time to generate PWM signals grows directly with the number of channels.

Common Mistake

[X] Wrong: "The time to generate PWM signals stays the same no matter how many channels there are."

[OK] Correct: Each channel needs its own comparison, so more channels mean more work and more time.

Interview Connect

Understanding how time grows with input size helps you explain system performance clearly and confidently in real projects.

Self-Check

"What if we increased the resolution of the carrier waveform instead of the number of channels? How would the time complexity change?"