Gettin low pass filter into arduino sketch

Projects Programming
7

You might be overthinking this.
The math notation is sometimes different from the source code.

Calculating the average with a low-pass filter is like this:

Average(T) = 0.99 * Avarage(T-1) + 0.01 * newValue

The newValue influences the average for 1%.
In the source code, the existing average can be taken, then add 1% of the new value and then store it in the same average variable.

average = 0.99 * average + 0.01 * newValue;

That average can be seen as the DC-offset, so the result is:

result = newValue - average;

Add a setup() and loop() and the sketch is finished:

float average;
const float strength = 0.99; 

void setup() 
{
}

void loop() 
{
  float newValue = (float) analogRead(A0);
  average = (strength * average) + ((1.0-strength) * newValue);
  float result = newValue - average;

  delay(10);
}
To make it visual, the Serial Plotter of the Arduino IDE can be used. I used the Wokwi simulator with this sketch: 
// Forum: https://forum.arduino.cc/t/gettin-low-pass-filter-into-arduino-sketch/1105548
// This Wokwi project:
//
// The heart beat sensor is not released yet, it may change.
//
// Not using:
//    w(t)=x(t)+∝∗w(t−1)
//    y(t)=w(t)−w(t−1)
//    y(t): is the output of the filter
//    x(t): current input/value
//    w(t): intermediate value, acts like the history of the DC value
//    α: is the response constant of the filter
//    If α = 1 then everything passes through
//    If α = 0 then nothing passes through
//
// Using a standard low-pass filter instead:
//    average = strength * average + (1 - strength) * newVale

float average;
const float strength = 0.995; 

void setup() 
{
  Serial.begin(115200);

  // Print 1 second where all the signals are zero.
  // This is only to make it look better on the Serial Plotter.
  // Not for the real application.
  for(int i=0; i<100; i++)
  {
    Serial.println( "0.0,0.0,0.0,0.0");
    delay(10);
  }
}

void loop() 
{
  float newValue = (float) analogRead(A0);
  average = (strength * average) + ((1.0-strength) * newValue);
  float result = newValue - average;

  Serial.print( "0.0");        // Green, show where the X-axis is
  Serial.print( ",");
  Serial.print( newValue);     // Orange
  Serial.print( ",");
  Serial.print( average);      // Violet
  Serial.print( ",");
  Serial.print( result);       // Cyan
  Serial.println();

  // A quick and dirty way to sample at regular intervals
  delay(10);
}

Try the sketch in Wokwi:

afbeelding
afbeelding833×532 28.6 KB

Green line: X-axis
Orange line: Heart Beat
Pink line: Average
Cyan line: Result: Heart Beat without DC-offset.