Question

I am trying to do a project in sound processing and need to put the frequencies into another domain. Now, I have tried to implement an FFT, that didn’t go well. I tried to understand the z-transform, that didn’t go to well either. I read up and found DFT’s a lot more simple to understand, especially the algorithm. So I coded the algorithm using examples but I do not know or think the output is right. (I don’t have Matlab on here, and cannot find any resources to test it) and wondered if you guys knew if I was going in the right direction. Here is my code so far:

#include <iostream>
#include <complex>
#include <vector>

using namespace std;

const double PI = 3.141592;

vector< complex<double> > DFT(vector< complex<double> >& theData)
{
// Define the Size of the read in vector
const int S = theData.size();

// Initalise new vector with size of S
vector< complex<double> > out(S, 0);
for(unsigned i=0; (i < S); i++)
{
    out[i] = complex<double>(0.0, 0.0);
    for(unsigned j=0; (j < S); j++)
    {
        out[i] += theData[j] * polar<double>(1.0, - 2 * PI * i * j / S);
    }
}

return out;
}

int main(int argc, char *argv[]) {

vector< complex<double> > numbers;

numbers.push_back(102023);
numbers.push_back(102023);
numbers.push_back(102023);
numbers.push_back(102023);

vector< complex<double> > testing = DFT(numbers);

for(unsigned i=0; (i < testing.size()); i++)
{
    cout << testing[i] << endl;

}
}

The inputs are:

102023               102023

102023               102023

And the result:

(408092,       0)

(-0.0666812,  -0.0666812)

(1.30764e-07, -0.133362)

(0.200044,    -0.200043)

Any help or advice would be great, I’m not expecting a lot, but, anything would be great. Thank you 🙂

Answer 1

Your code looks okey. out[0] should represent the “DC” component of your input waveform. In your case, it is 4 times bigger than the input waveform, because your normalization coefficient is 1.

The other coefficients should represent the amplitude and phase of your input waveform. The coefficients are mirrored, i.e., out[i] == out[N-i]. You can test this with the following code:

double frequency = 1; /* use other values like 2, 3, 4 etc. */
for (int i = 0; i < 16; i++)
    numbers.push_back(sin((double)i / 16 * frequency * 2 * PI));

For frequency = 1, this gives:

(6.53592e-07,0)
(6.53592e-07,-8)
(6.53592e-07,1.75661e-07)
(6.53591e-07,2.70728e-07)
(6.5359e-07,3.75466e-07)
(6.5359e-07,4.95006e-07)
(6.53588e-07,6.36767e-07)
(6.53587e-07,8.12183e-07)
(6.53584e-07,1.04006e-06)
(6.53581e-07,1.35364e-06)
(6.53576e-07,1.81691e-06)
(6.53568e-07,2.56792e-06)
(6.53553e-07,3.95615e-06)
(6.53519e-07,7.1238e-06)
(6.53402e-07,1.82855e-05)
(-8.30058e-05,7.99999)

which seems correct to me: negligible DC, amplitude 8 for 1st harmonics, negligible amplitudes for other harmonics.