How to calculate the cut-off frequency of a software average filter

Question

I want to read the voltage of a battery using an ADC connected to a PLC. The signal oscillates a bit and I want to smooth it. The ADC samples the signal at 860 samples per second and stores it in variable ADCValue. Then I take an ADCValue every 0.5 seconds to create an array of size four and finally every two seconds I do an average of these four values.

My understanding is that this averaging by software is equivalent to a low pass filter. Is this correct? If so, how do I calculate the cut-off frequency of it?.

Edit: find here the Arduino code related to this, which uses two timers that call the interrupt functions associated in the setup():

#include <TimerOne.h>
#include <TimerThree.h>
#include <Wire.h>

const int AVGNUMELEM = 4;
float  ADCValue ; // This value comes from an external ADC and it is configured at 860 SPS
float arrayAvg[AVGNUMELEM];
float avg = 0;
int counteravg = 0;

//2 seconds
const long TIMER1TIME = 2000000;
//0.5 seconds
const long TIMER3TIME = 500000;

// Timer called every 0.5 seconds
void ISR_Store4values() {

  if(counteravg < AVGNUMELEM){
    arrayAvg[counteravg] = ADCValue;
    counteravg ++;
  }
  else
  {  
    for(int i = 0; i < (AVGNUMELEM-1); i++){
      arrayAvg[i] = arrayAvg[i + 1];
    }
    arrayAvg[(AVGNUMELEM-1)] = ADCValue;
  }
}

// Timer called to compute the average every 2 seconds
void ISR_PrintEvery2s() {
 
  avg = 0;
  for(int i = 0; i < AVGNUMELEM; i++){
    avg = avg + arrayAvg[i];
  }
  avg = avg / AVGNUMELEM;

  Serial.print(avg,4);
}

void setup() {

  Timer1.initialize(TIMER1TIME);
  Timer1.attachInterrupt(ISR_PrintEvery2s); 

  Timer3.initialize(TIMER3TIME);
  Timer3.attachInterrupt(ISR_Store4values); 

}

void loop() {

}

Answer 1

It sounds like you are doing straight up accumulate-and-dump, which is a downsampled moving average, which is a finite-impulse response (FIR) filter with equal tap weights. Some people call it a frequency-domain sinc filter.

From your description you have 4 taps and a sampling period of 0.5 second. It is straight forward to find an analytical solution for your problem, but a quick solution is to compute it numerically in e.g. Octave:

pkg load control % loading the control toolbox
H = tf([1 1 1 1],[4 0 0 0],0.5,'Variable','z^-1'); % set up transfer-function in z-domain for a 4 tap moving average with sampling-time 0.5 s
[MAG,PHASE,W] = bode(H); % compute magnitude and phase response, using automatically generated frequency vector W
W(min(find(MAG < 0.7079)))/(2*pi) % approx. bandwidth at -3 dB in Hz, found by selecting all values for the magnitude less than 0.709 (-3 dB) and then picking the lowest frequency value the fulfills the criteria