Why PWM is needed for analog-like control in Raspberry Pi - Performance Analysis

Time Complexity: Why PWM is needed for analog-like control

O(n)

Understanding Time Complexity

We want to understand how the time cost changes when using PWM to mimic analog control on a Raspberry Pi.

How does the program's work grow as we change the PWM signal length or frequency?

Scenario Under Consideration

Analyze the time complexity of this PWM signal generation code.

import RPi.GPIO as GPIO
import time

GPIO.setmode(GPIO.BCM)
GPIO.setup(18, GPIO.OUT)
pwm = GPIO.PWM(18, 1000)  # 1kHz frequency
pwm.start(50)  # 50% duty cycle

try:
    while True:
        time.sleep(1)
except KeyboardInterrupt:
    pwm.stop()
    GPIO.cleanup()

This code sets up a PWM signal on pin 18 with a 1kHz frequency and 50% duty cycle, running continuously.

Identify Repeating Operations

Look at what repeats in this PWM control.

• Primary operation: The PWM hardware or software toggles the pin on and off repeatedly to create the signal.
• How many times: This toggling happens thousands of times per second, depending on the frequency.

How Execution Grows With Input

The number of toggles grows directly with the PWM frequency and duration.

Input Size (frequency in Hz)	Approx. Operations per second
10	20 toggles (on and off)
1000	2000 toggles
10000	20000 toggles

Pattern observation: As frequency increases, the toggling operations increase linearly, meaning more work per second.

Final Time Complexity

Time Complexity: O(n)

This means the work grows linearly with the number of PWM cycles per second.

Common Mistake

[X] Wrong: "PWM toggling happens only once or a few times regardless of frequency."

[OK] Correct: The pin must switch on and off every cycle, so higher frequency means many more toggles and more work.

Interview Connect

Understanding how PWM timing affects processing helps you explain real hardware control and efficient coding on devices like Raspberry Pi.

Self-Check

What if we changed the PWM frequency from 1kHz to 10kHz? How would the time complexity change?