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;
    }