fft.txt

基为2的快速傅立叶变换的核心代码

void FFT(complex<double> * TD, complex<double> * FD, int r)
{
	// 付立叶变换点数
	LONG	count;
	
	// 循环变量
	int		i,j,k;
	
	// 中间变量
	int		bfsize,p;
	
	// 角度
	double	angle;
	
	complex<double> *W,*X1,*X2,*X;
	
	// 计算付立叶变换点数
	count = 1 << r;
	
	// 分配运算所需存储器
	W  = new complex<double>[count / 2];
	X1 = new complex<double>[count];
	X2 = new complex<double>[count];
	
	// 计算加权系数
	for(i = 0; i < count / 2; i++)
	{
		angle = -i * PI * 2 / count;
		W[i] = complex<double> (cos(angle), sin(angle));
	}
	
	// 将时域点写入X1
	memcpy(X1, TD, sizeof(complex<double>) * count);
	
	// 采用蝶形算法进行快速付立叶变换
	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];
	}
	
	// 释放内存
	delete W;
	delete X1;
	delete X2;
}