The Moving Average Trend Spotter

SS 1 Arduino Uno Simulation first | Statistical Signal Filtering

📑 Project sections ▾

Simulation lab Build guide Learn & Story Test model Try a challenge Quick check & Quiz

Simulation lab

Board: ♾️ Arduino Uno

⛶ Expand Open in Wokwi ↗

▶ Run simulation ■ ↻

diagram.json sketch.ino >_ Serial monitor

Simulator preview

Press the pushbutton to test the interactive circuit in real time.

>_ Serial monitor Clear

Ready — press the button.

📦 Components ▴

• Arduino Uno microcontroller board
• LED indicator (green)
• 220 ohm current-limiting resistor
• Tactile pushbutton switch
• Jumper wires (male-male)

📖 Learn 🔧 Build </> Code ▷ Test ⚑ Challenge ❓ Quiz

🔧 Build Your Moving Average Filter

1 Construct a circular buffer array of length 10 in Arduino C++: 'int window[10]'.

2 Maintain a running sum variable to achieve O(1) constant-time algorithmic updates.

3 Sample analog input A0; subtract the oldest value, overwrite with new reading, and add to sum.

4 Verify on the Wokwi Serial Plotter that high-frequency ADC thermal ripple is cleanly eliminated!

🧩 Block plan / Starter code ▴

const int SENSOR_PIN = A0;
const int WINDOW_SIZE = 10;

int readings[WINDOW_SIZE];
int readIndex = 0;
long runningSum = 0;
int smoothedValue = 0;

void setup() {
  Serial.begin(115200);
  for (int i = 0; i < WINDOW_SIZE; i++) {
    readings[i] = analogRead(SENSOR_PIN);
    runningSum += readings[i];
  }
  Serial.println("Raw,Smoothed");
}

void loop() {
  int rawReading = analogRead(SENSOR_PIN);

  // Constant-time O(1) circular buffer update
  runningSum -= readings[readIndex];
  readings[readIndex] = rawReading;
  runningSum += readings[readIndex];
  readIndex = (readIndex + 1) % WINDOW_SIZE;

  smoothedValue = runningSum / WINDOW_SIZE;

  Serial.print(rawReading);
  Serial.print(",");
  Serial.println(smoothedValue);
  delay(50);
}

Maintaining runningSum enables O(1) updates without expensive iterative array looping in embedded memory.

⚗️ Test your model

Test Condition / Action	Expected Result
Thermal ADC Noise (±15 raw counts)	Smoothed output variance drops to < ±1 count
Sudden Step Input (+200 counts)	Smoothed output cleanly ramps to new level over exactly 10 samples
Sustained DC Input	Zero steady-state error; smoothed output matches mean raw input

⚑ Try a challenge

Calculate and output the real-time sample variance in the loop to identify when the sensor has entered a turbulent state!

❓ Quick check

Why do raw analog sensor readings from an Arduino ADC fluctuate randomly by a few counts even in a stationary environment?

• Thermal noise, power supply ripple, and electromagnetic interference create small electrical fluctuations in the analog signal
• The Arduino CPU is broken

Check answer

📖 Our Story & Concepts

Analog-to-Digital Converters (ADCs) in microcontrollers convert continuous physical voltages into discrete integer counts. In real circuits, power supply ripple, electromagnetic interference (EMI), and thermal agitation induce high-frequency white noise.

In medical electrocardiograms (ECGs) and industrial thermal kilns, calculating an N-point Simple Moving Average (SMA) acts as an optimal finite impulse response (FIR) low-pass filter. Implementing this with a circular ring buffer ensures execution time remains independent of window length.

</> Full Annotated Code Walkthrough

// Complete Circular Buffer with Real-Time Statistical Variance
const int SENSOR_PIN = A0;
const int N = 10;

int buf[N];
int idx = 0;
long sum = 0;

void setup() {
  Serial.begin(115200);
  for (int i = 0; i < N; i++) {
    buf[i] = analogRead(SENSOR_PIN);
    sum += buf[i];
  }
}

void loop() {
  int raw = analogRead(SENSOR_PIN);
  sum -= buf[idx];
  buf[idx] = raw;
  sum += buf[idx];
  idx = (idx + 1) % N;

  float mean = (float)sum / N;

  // Compute Variance
  float varSum = 0;
  for (int i = 0; i < N; i++) {
    float diff = buf[i] - mean;
    varSum += diff * diff;
  }
  float variance = varSum / N;

  Serial.print("Raw:"); Serial.print(raw);
  Serial.print(",Mean:"); Serial.print(mean);
  Serial.print(",Variance:"); Serial.println(variance);
  delay(100);
}

Maintaining runningSum enables O(1) updates without expensive iterative array looping in embedded memory.

▷ Expected Results & Troubleshooting

Test Condition / Action	Expected Result
Thermal ADC Noise (±15 raw counts)	Smoothed output variance drops to < ±1 count
Sudden Step Input (+200 counts)	Smoothed output cleanly ramps to new level over exactly 10 samples
Sustained DC Input	Zero steady-state error; smoothed output matches mean raw input

⚑ Extension Challenges & Blueprints

⚑ Extension Challenges

• Level 1: Implement an Exponential Moving Average (EMA) with configurable smoothing factor alpha (0.1 to 0.9).
• Level 2: Benchmark CPU execution cycles between circular buffer O(1) and array recalculation O(N).
• Level 3: Apply the filter to an ultrasonic rangefinder to eliminate acoustic reflection spikes.

❓ Check Your Understanding

Question 1: Why do raw analog sensor readings from an Arduino ADC fluctuate randomly by a few counts even in a stationary environment?

• Thermal noise, power supply ripple, and electromagnetic interference create small electrical fluctuations in the analog signal
• The Arduino CPU is broken
• The breadboard wires are made of rubber
• The sensor only works when shaken

Question 2: How does a circular buffer array in C/C++ work when a new sensor sample arrives?

• It overwrites the oldest sample in the array and advances the index circularly using the modulo operator (index = (index + 1) % N)
• It deletes the entire microcontroller memory
• It doubles the array size infinitely until RAM is exhausted
• It reverses the alphabet

Question 3: If the window size N is chosen to be 100 samples instead of 5 samples, what is the engineering tradeoff?

• The filtered signal becomes much smoother, but responds more slowly (higher lag) to genuine sudden changes
• The Arduino will run out of power
• The sensor reads negative numbers
• The C++ compiler refuses to compile

Question 4: What pin on the Arduino Uno is used to read the variable analog voltage from a temperature sensor or potentiometer?

• Analog Pin A0 (or A1–A5)
• Digital Pin 0 (RX)
• RESET Pin
• GND Pin

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