/* 函數名稱：FFT()
* 參數:
* complex<double> * TD - 指向時域數組的指針
* complex<double> * FD - 指向頻域數組的指針
* r －2的冪數，即迭代次數
* 返回值: 無。
* 說明:該函數用來實現快速傅立葉變換
*/
#include "StdAfx.h"
#include "fft.h"


void __stdcall FFT(complex<double> * TD, complex<double> * FD, int r)
{ 
   LONG count; 
// 傅立葉變換點數

   int i,j,k; // 循環變量
   int bfsize,p; // 中間變量
   double angle; // 角度 
   complex<double> *W,*X1,*X2,*X;
   count = 1 << r; //傅立葉變換點數

// 分配運算所需存儲器

   W = new complex<double>[count / 2];
   X1 = new complex<double>[count];
   X2 = new complex<double>[count];

// 計算加權系數

   for(i = 0; i < count / 2; i++)
   {
     angle = -i * PI * 2 / count;
     W[i] = complex<double> (cos(angle), sin(angle));
   }

// 將時域點寫入X1

   memcpy(X1, TD, sizeof(complex<double>) * count);

// 采用蝶形算法進行快速傅立葉變換

  for(k = 0; k < r; k++)
  {
      for(j = 0; j < 1 << k; j++)
	  {
        bfsize = 1 << (r-k);
        for(i = 0; i < bfsize / 2; i++)
		{
          p = j * bfsize;
          X2[i + p] = X1[i + p] + X1[i + p + bfsize / 2];
          X2[i + p + bfsize / 2] = (X1[i + p] - X1[i + p + bfsize / 2]) * W[i * (1<<k)];
		}
	  }
     X = X1;
     X1 = X2;
     X2 = X;
  }

// 重新排序
     for(j = 0; j < count; j++)
	 {
        p = 0;
        for(i = 0; i < r; i++)
		{
          if (j&(1<<i))
		  {
            p+=1<<(r-i-1);
		  }
		}
        FD[j]=X1[p];
	 }

// 釋放內存

    delete W;
    delete X1;
    delete X2;
}