Hello,
I'm tryung to implement Fast Fourier Transformation. And I'm not sure if I understand it correctly.

As I understand when I transform (for example) simple sine wave by FFT, and than make inversion I should get exactly the same sine wave. Am I right?

But in some way it doesn't work for me. I found that code with the friend google:

Qt Code: 
  1. #include <complex>
  2. #include <iostream>
  3. #include <valarray>
  4. #include <QVector>
  5. using namespace std;
  6.  
  7. const double PI = 3.141592653589793238460;
  8.  
  9. typedef std::complex<double> Complex;
  10. typedef std::valarray<Complex> CArray;
  11.  
  12. // Cooley–Tukey FFT (in-place, divide-and-conquer)
  13. // Higher memory requirements and redundancy although more intuitive
  14. void fft(CArray& x)
  15. {
  16.     const size_t N = x.size();
  17.     if (N <= 1) return;
  18.  
  19.     // divide
  20.     CArray even = x[std::slice(0, N/2, 2)];
  21.     CArray  odd = x[std::slice(1, N/2, 2)];
  22.  
  23.     // conquer
  24.     fft(even);
  25.     fft(odd);
  26.  
  27.     // combine
  28.     for (size_t k = 0; k < N/2; ++k)
  29.     {
  30.         Complex t = std::polar(1.0, -2 * PI * k / N) * odd[k];
  31.         x[k    ] = even[k] + t;
  32.         x[k+N/2] = even[k] - t;
  33.     }
  34. }
  35.  
  36. // inverse fft (in-place)
  37. void ifft(CArray& x)
  38. {
  39.     // conjugate the complex numbers
  40.     x = x.apply(std::conj);
  41.  
  42.     // forward fft
  43.     fft( x );
  44.  
  45.     // conjugate the complex numbers again
  46.     x = x.apply(std::conj);
  47.  
  48.     // scale the numbers
  49.     x /= x.size();
  50. }
  51.  
  52. int main()
  53. {
  54.     const Complex test[] = { 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 };
  55.     CArray data(test, 8);
  56.  
  57.     // forward fft
  58.     fft(data);
  59.  
  60.     std::cout << "fft" << std::endl;
  61.     for (int i = 0; i < 10; ++i)
  62.     {
  63.         std::cout << data[i] << std::endl;
  64.     }
  65.  
  66.     // inverse fft
  67.     ifft(data);
  68.  
  69.     std::cout << std::endl << "ifft" << std::endl;
  70.     for (int i = 0; i < 10; ++i)
  71.     {
  72.         std::cout << data[i] << std::endl;
  73.     }
  74.     return 0;
  75. }
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So as I understand by ifft(data) I should receive the same as it was on the beggining, but the results are quite different. Can anyone help me?
For any help thanks in advance.
Best Regards