fft的实现

     private static Complex[] FFT1(Complex[] f)
     {
         int N=f.length;
         int power= (int) (Math.log10(N)/Math.log10(2));
         Complex[] F=new Complex[N];
         //按奇偶分组
         for(int i=0;i<N;i++)
         {
             int p = 0;
             for (int j = 0; j < power; j++)
                 if ((i & (1 << j)) != 0)
                     p += 1 << (power - j - 1);  
 
             F[p] = f[i];
         }
         //蝶形因子
         Complex[] wc = new Complex[N/ 2];
         for (int i = 0; i < N / 2; i++)
         {
             double angle = -i * Math.PI * 2 / N;
             wc[i]=new Complex(Math.cos(angle),Math.sin(angle));
         }
         //蝶形运算
         for(int L=1;L<=power;L++)//第L层数
         {
             int bf=1<<(power-L);//蝶形数
             for(int n=0;n<bf;n++)//第n+1个蝶形
             {
                 int bfsize=1<<L;//蝶形大小
                 for(int k=0;k<bfsize/2;k++)//第k+1个蝶形因子
                 {
                     Complex temp,X1,X2;;
                     int i=n*bfsize+k,
                         j=i+bfsize/2;
                     temp=wc[k*bf].Mul(F[j]);
                     X1=F[i].Add(temp);
                     X2=F[i].Sub(temp);
                     F[i]=X1;
                     F[j]=X2;
                 }
             }
         }
         return F;
     }