Discrete Fourier Transform Test Results

[DavyS]

Hello. I have been testing my Discrete Fourier Transform program for 1 dimensional data (written in using C++).

For the following test input data(X), the corresponding DFT(X) output is expected. The first number in each separate column is the REAL and the second number is the IMAGINARY.

          

X                      DFT X 
( 1.000, 0.000) ( 4.000, 0.000)
( 1.000, 0.000) ( 1.000,-2.414)
( 1.000, 0.000) ( 0.000, 0.000)
( 1.000, 0.000) ( 1.000,-0.414)
( 0.000, 0.000) ( 0.000, 0.000)
( 0.000, 0.000) ( 1.000, 0.414)
( 0.000, 0.000) ( 0.000, 0.000)
( 0.000, 0.000) ( 1.000, 2.414)

My program produces the output below for the same input test data.

(0.5, 0)
(0.125,  -0.302)
(-2.3e-017, -2.78e-017)
(0.125, -0.0518)
(0, -3.06e-017)
(0.125, 0.0518)
(4.11e-017, -4.16e-017)
(0.125, 0.302)

The program code is below. I would appreciate to learn where the error lies and how to fix this, thank you!

bool inverse = false;
int n = 8;
double gRe[8] = {0,1,0,0,0,0,0,0};
double gIm[8] = {0,0,0,0,0,0,0,0};
double GRe[8] = {0,0,0,0,0,0,0,0};
double GIm[8] = {0,0,0,0,0,0,0,0};
 

for(int w = 0; w < n; w++)
{
  GRe[w] = GIm[w] = 0;
  for(int x = 0; x < n; x++)
  {
    double a = -2 * pi * w * x / float(n);
    if(inverse) a = -a;
    double ca = cos(a);
    double sa = sin(a);
    GRe[w] += gRe[x] * ca - gIm[x] * sa;
    GIm[w] += gRe[x] * sa + gIm[x] * ca;
  }
  if(!inverse)
  {
    GRe[w] /= n;
    GIm[w] /= n;
  }
}

fstream DFTdata;
DFTdata.open("DFT_Bdata.txt");
for (int i = 0; i<n; i++) // width  
{
   DFTdata <<"Input: "<< testReal[i]
	             <<" Real: "<< setprecision(3)<<FReal[i] <<" Imag:  "<<setprecision(3)<<FIma[i]<< endl;
}
	
DFTdata.close();