Finding RMS value of arrays.

[EagleScreams]

Hi, I'm very new to C++ and can't seem to work out why this piece of code wont work as i expected.

I have three arrays representing wave functions and i am trying to find out the averages and RMS values for each waves. The RMS seems to be eluding me.

#include <iostream>
#include <cmath>

using namespace std;

#define SIZE1 80
#define SIZE2 62
#define SIZE3 29

double getAverage(short arr[], int size)

{
  int    i, sum = 0;
  double avg;

  for (i = 0; i < size; ++i)
  {
    sum += arr[i];
   }

  avg = double(sum) / size;

  return avg;
}

double getRMS (short arr[], int size)

{
    int i;
    double sumsq;
    double RMS;
    sumsq = 0;


    for (i = 0; i< size; i++)
    {
        sumsq += arr[i]*arr[i];
        RMS = (1/size)*(sqrt(sumsq));

        return RMS;
    }

}

int main()
{
    short cosine[SIZE1] = {
        32767, 32666, 32364, 31862, 31163, 30273, 29196, 27938, 26509, 24916,
        23170, 21280, 19260, 17121, 14876, 12539, 10126, 7649, 5126, 2571,
        0, -2571, -5126, -7649, -10126, -12539, -14876, -17121, -19260, -21280,
        -23170, -24916, -26509, -27938, -29196, -30273, -31163, -31862, -32364, -32666,
        -32767, -32666, -32364, -31862, -31163, -30273, -29196, -27938, -26509, -24916,
        -23170, -21280, -19260, -17121, -14876, -12539, -10126, -7649, -5126, -2571,
        0, 2571, 5126, 7649, 10126, 12539, 14876, 17121, 19260, 21280,
        23170, 24916, 26509, 27938, 29196, 30273, 31163, 31862, 32364, 32666
    };
    short triangle[SIZE2] = {
        15500, 14500, 13500, 12500, 11500, 10500, 9500, 8500, 7500, 6500,
        5500, 4500, 3500, 2500, 1500, 500, -500, -1500, -2500, -3500,
        -4500, -5500, -6500, -7500, -8500, -9500, -10500, -11500, -12500, -13500,
        -14500, -15500, -14500, -13500, -12500, -11500, -10500, -9500, -8500, -7500,
        -6500, -5500, -4500, -3500, -2500, -1500, -500, 500, 1500, 2500,
        3500, 4500, 5500, 6500, 7500, 8500, 9500, 10500, 11500, 12500,
        13500, 14500
    };
    short sawtooth[SIZE3] = {
        -24000, -22000, -20000, -18000, -16000, -14000, -12000, -10000, -8000, -6000,
        -4000, -2000, 0, 2000, 4000, 6000, 8000, 10000, 12000, 14000,
        16000, 18000, 20000, 22000, 24000, 26000, 28000, 30000, 32000
    };

cout<<"Average of cosine:  "<<getAverage (cosine,SIZE1)<<endl;

cout<<"Average of traingle:  "<<getAverage (triangle,SIZE2)<<endl;

cout<< "Average of sawtooth:  "<<getAverage(sawtooth,SIZE3)<<endl;

cout<<"RMS of cosine"<<getRMS (cosine,SIZE1) <<endl;

return 0;
}

The values for averages are what i would expect, but the value for RMS cosine is found to be 0. Having gone through the array using a calculator i expect a value of roughly 408.

Any tips would be hugely appreciated.


edit: Equation to find RMS is ( 1/size of array * (sum of squares))^1/2

[o3hC5Di1]

Hi there,

I believe you problem lies here:

RMS = (1/size)*(sqrt(sumsq)); //line 39 

You probably mean:

RMS = (static_cast<double>(1)/size)*(sqrt(sumsq));

If you don't cast 1 (or size) to a double, 1/size will be an integer by integer division, returning an integer result (0 in this case, because 1 divided by size will be 0. something).


Hope that helps.

All the best,
NwN

[OxBADC0DE]

if your formula for RMS is correct, then RMS shouldn't be within the body of the for...loop, you should have:

sumsq=0;
for(int x=0; x<size;x++)
{
//sum of all squares
sumsq+=(array[x]*array[x]);
}
RMS= everything_goes_here;
return RMS

[D80DSL3A]

In addition to the points above, shouldn't it be
RMS = static_cast<double>(sqrt(sumsq/size)); ?

You may have an overflow issue with the product of 2 shorts on line 38
sumsq += arr[i]*arr[i];
Consider building up the product in an int variable first:

int prod = arr[i];
prod *= arr[i];
sumsq += prod;

[EagleScreams]

Thank you all for your replies. Having taken your suggestions into account and changed the code to:

double getRMS (short arr[], int size)

{
    int i;
    double sumsq;
    double RMS;
    sumsq = 0;


    for (i = 0; i< size; i++)
    {
        sumsq += arr[i]*arr[i];
    }
    RMS = sqrt((static_cast<double>(1)/size)*(sumsq));
    return RMS;
}

I am finding RMScosine to be 23169 and as I said above i think it should be around 408.

[D80DSL3A]

You may not have seen my post when you last posted. Try fixing the overflow problem mentioned there.

[Chervil]

The RMS value of a pure sine wave (or cosine wave) is equal to the peak value divided by sqrt(2).

Thus, if the peak value is 32767, the RMS value should be 32767/sqrt(2) = 23169.8

http://en.wikipedia.org/wiki/Root_mean_square

[EagleScreams]

Thanks for your useful hints.