// compute DFT magnitude from input samples

#include <stdio.h>
#include <math.h>

#define N 256
#define N2 ((N/2)+1)

int main( int argc, char *argv[])
{
  double C[N2] = { 0 }, S[N2] = { 0 }, pi = 4*atan(1), x, wk;
  int s, j, k = 0, twoflag = 0;

 // check for command-line argument "2"
 // indicating 2-column input
 //
  if( argc > 1 && argv[1][0] == '2')
    twoflag = 1;

  while(1) // until error or EOF
  {
   // with 2-column input, the first column is ignored
   //
    if( twoflag) s = scanf( "%lf", &x);

    s = scanf( "%lf", &x);

    if( s < 0) break;

    if( s != 1)
    {
      fprintf( stderr, "dft: bad input data\n");
      break;
    }

    for( j = 0; j < N2; ++j)
    {
      wk = (2*pi*j/N)*k;
      C[j] += x*cos(wk);
      S[j] += x*sin(wk);
    }
    ++k;
  }

  for( j = 0; j < N2; ++j)
    printf( "%g %g\n", j*8000.0/N, sqrt(C[j]*C[j]+S[j]*S[j]) );

  return 0;
}