Measure moving-average smoothing and lag

Observe how a five-sample moving average suppresses variation while delaying a genuine DHT22 temperature change.

Physics Phoebe: I want you to compare every raw step with its delayed average before choosing a window., your practice guide

Physics Phoebe: I want you to compare every raw step with its delayed average before choosing a window.
Predict the reading, then compare it with the measurement.

Wokwi ESP32

Third party Tool

Observe how a five-sample moving average suppresses variation while delaying a genuine DHT22 temperature change.

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Version tested: Compiled and booted by the Wokwi gate (ESP32 Arduino core 3.3.11); captured in the Wokwi web editor on 2026-09-09. Date: 2026-09-09.

Open the ESP32 editor, paste diagram.json, then paste sketch.ino.

Open Wokwi to paste in the files (new tab)

Get the files

Use both prepared files. This is a paste-in setup; saving a project requires a Wokwi account.

diagram.json

793 bytes · Circuit connections

Download

sketch.ino

1,220 bytes · ESP32 program

Download

#include <DHT.h>

constexpr uint8_t DHT_PIN = 4;
constexpr uint8_t WINDOW_SIZE = 5;
DHT dht(DHT_PIN, DHT22);

float temperatures[WINDOW_SIZE] = {};
float humidities[WINDOW_SIZE] = {};
uint8_t writeIndex = 0;
uint8_t sampleCount = 0;

void setup() {
  Serial.begin(115200);
  dht.begin();
  Serial.println("DHT FILTER window=5 interval=2000ms");
}

void loop() {
  const float temperature = dht.readTemperature();
  const float humidity = dht.readHumidity();

if (isnan(temperature) || isnan(humidity)) {
    Serial.println("DHT ERROR invalid reading discarded");
    delay(2000);
    return;
  }

temperatures[writeIndex] = temperature;
  humidities[writeIndex] = humidity;
  writeIndex = (writeIndex + 1) % WINDOW_SIZE;
  if (sampleCount < WINDOW_SIZE) sampleCount++;

float temperatureTotal = 0.0f;
  float humidityTotal = 0.0f;
  for (uint8_t i = 0; i < sampleCount; i++) {
    temperatureTotal += temperatures[i];
    humidityTotal += humidities[i];
  }

Serial.printf(
    "FILTER rawT=%.1fC rawRH=%.1f%% avgT=%.1fC avgRH=%.1f%% n=%u\n",
    temperature, humidity, temperatureTotal / sampleCount,
    humidityTotal / sampleCount, sampleCount
  );
  delay(2000);  // DHT22 needs two seconds between reads.
}

Use the launch button above to open the ESP32 editor in Wokwi.
Select the editor’s diagram.json tab and replace all its text with the supplied diagram.json.
Select the sketch.ino tab, replace all its text with the supplied sketch.ino, then click Start Simulation.

Steps

Screens captured against Wokwi ESP32 Compiled and booted by the Wokwi gate (ESP32 Arduino core 3.3.11); captured in the Wokwi web editor on 2026-09-09 on 2026-09-09; the tool may have moved on — the text steps are the contract.

Step 1
Do
Paste diagram.json and sketch.ino into a new Wokwi ESP32 project, then trace power, ground, data, and the pull-up.
You will see
The DHT22 data pin reaches GPIO4 and a 10 kOhm resistor pulls that signal to 3.3 V.
Why it matters
The wiring reproduces the source lab's electrical precondition before software filtering is evaluated.
Step 2
Do
Inspect the circular buffer, valid-sample count, and two-second delay in sketch.ino.
You will see
The code stores five readings, averages only initialized entries, and waits for the DHT22's required interval.
Why it matters
Counting only valid entries avoids startup bias from zero-filled slots, while the interval prevents oversampling.
Step 3
Do
Start the simulation and open Serial Monitor at 115200 baud.
You will see
The sketch announces a five-sample window and 2000 ms interval.
Why it matters
Recording filter configuration makes each output trace reproducible.
Step 4
Do
Leave the DHT22 at 24 degrees C and 40 percent relative humidity until the baseline prints.
You will see
Raw and average values both settle at 24.0 degrees C and 40.0 percent.
Why it matters
A steady baseline confirms the filter is not inventing an offset.
Step 5
Do
Select the DHT22 and change its temperature to 30 degrees C; inspect the first changed sample.
You will see
The raw temperature reaches 30.0 degrees C while the five-sample average remains between 24 and 30 degrees C.
Why it matters
The gap is the filter's response lag, not measurement error.
Step 6
Do
Keep the temperature at 30 degrees C for two more sample intervals.
You will see
Successive 30.0 degree C inputs pull the average upward toward the new steady value.
Why it matters
A window reduces random variation by combining samples, but necessarily spreads a real step across time.
Step 7
Do
Set relative humidity to 70 percent and inspect the next output.
You will see
Raw humidity changes independently to 70.0 percent while its average begins below 70 percent.
Why it matters
Independent channels need independent buffers, and each exhibits the same smoothing-versus-lag tradeoff.

Chapter checks

These questions refer to the chapter’s examples. Use the return links to review their answers.

You have a noisy temperature sensor that occasionally produces spike values (e.g., 22C, 23C, 55C, 22C). Which filter is better for removing these spikes?
Return to the chapter’s knowledge check
What is the main advantage of a Kalman filter over a simple moving average filter?
Return to the chapter’s knowledge check
For a moving average filter with window size N=10 sampling at 100Hz, what is the approximate latency introduced?
Return to the chapter’s knowledge check

Return to Sensor Filtering and Validation · Browse Labs

Wokwi ESP32

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diagram.json

sketch.ino

Steps

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Chapter checks

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