离散傅里叶变换C++代码

/*
 * myfft.h
 */

#ifndef __MYFFT_H__
#define __MYFFT_H__

#include 


typedef struct _my_complex
{
	double r; //复数实部
	double i; //复数虚部

	_my_complex(){}
	_my_complex(double _r, double _i){r = _r; i = _i;}
	~_my_complex(){}

	_my_complex operator + (const _my_complex & c) //重载加号运算符
	{
		return _my_complex(r + c.r, i + c.i);
	}
	
	_my_complex operator - (const _my_complex & c) //重载减号运算符
	{
		return _my_complex(r - c.r, i - c.i);
	}

	_my_complex operator * (const _my_complex & c) //重载乘号运算符
	{
		return _my_complex(r * c.r - i * c.i, r * c.i + i * c.r);
	}
}my_complex;


int myfft_by_define_c2c_1d(my_complex * in, int n1, my_complex * out, int n2, int line_width = 1, int is_inv = 0); //按照定义进行一维复数离散傅里叶变换
int myfft_by_define_c2c_2d(my_complex * in, int m, int n, int is_inv = 0); //按照定义进行二维复数离散傅里叶变换

int myfft_c2c_1d_base2(my_complex * in, int n, int line_width = 1, int is_inv = 0); //进行一维复数离散快速傅里叶变换(基2)

int print_complex_array_1d(my_complex * in, int n);
int print_complex_array_2d(my_complex * in, int m, int n);


#endif //__MYFFT_H__

/*
 * myfft.cpp
 */

#include 
#include 
#include 
#include "myfft.h"

#define PI 3.1415926


/*------------按照定义进行一维复数离散傅里叶变换----------------------------------------
 * 原理：
 *     一维离散傅里叶变换公式为： X[k] = ∑x[n]*e^(-2πi * nk/N)，其中n=0,1,2,...,N-1
 *     一维离散傅里叶逆变换公式为： x[n] = 1/N * ∑X[k]*e^(2πi * nk/N)，其中k=0,1,2,...,N-1
 *     欧拉公式：e^ix = cos(x) + isin(x)
 *
 * 参数1：in            输入的一维复数数组
 * 参数2：n1            输入的一维复数数组的长度
 * 参数3：out           输出的一维复数数组
 * 参数4：n2            输出的一维复数数组的长度(必须和n1相等)
 * 参数5：line_width    数组下标的间隔(默认为1)，对于行变换等于1，对于列变换等于一行的宽度
 * 参数6：is_inv        是否是逆变换(默认不是)
 *
 * 过客 & [email protected] & 2016.01.25
 */
int myfft_by_define_c2c_1d(my_complex * in, int n1, my_complex * out, int n2, int line_width/*=1*/, int is_inv/*=0*/)
{
	if(n1 != n2){return 0;}

	double _2PI_N = 2.0 * PI / n1;

	if(is_inv == 0) //正变换
	{
		for(int m = 0; m < n1; m++)
		{
			int M = m * line_width;
			for(int k = 0; k < n1; k++ )
			{
				int K = k * line_width;
				out[M].r += in[K].r * cos(_2PI_N * m * k) + in[K].i * sin(_2PI_N * m * k); //计算实部
				out[M].i += -in[K].r * sin(_2PI_N * m * k) + in[K].i * cos(_2PI_N * m * k); //计算虚部
			}
		}
	}else if(is_inv == 1) //逆变换
	{
		for(int m = 0; m < n1; m++)
		{
			int M = m * line_width;
			for(int k = 0; k < n1; k++ )
			{
				int K = k * line_width;
				out[M].r += in[K].r * cos(_2PI_N * m * k) - in[K].i * sin(_2PI_N * m * k); //计算实部
				out[M].i += in[K].r * sin(_2PI_N * m * k) + in[K].i * cos(_2PI_N * m * k); //计算虚部
			}
			out[M].r /= n1; //归一化
			out[M].i /= n1; //归一化
		}
	}

	return 1;
}


//按照定义进行二维复数离散傅里叶变换
int myfft_by_define_c2c_2d(my_complex * in, int m, int n, int is_inv/*=0*/)
{
	my_complex * temp = new my_complex[m * n];
	memset(temp, 0, sizeof(my_complex) * m * n);

	for(int y = 0; y < n; y++) //先行变换
	{
		myfft_by_define_c2c_1d(in + y * n, n, temp + y * n, n, 1, is_inv);
	}

	memset(in, 0, sizeof(my_complex) * m * n);
	for(int x = 0; x < m; x++) //再列变换
	{
		myfft_by_define_c2c_1d(temp + x, m, in + x, m, n, is_inv);
	}

	delete [] temp; temp = NULL;

	return 1;
}


/*------------进行一维复数离散快速傅里叶变换(基2)----------------------------------------
 * 原理：
 *     对于FFT算法，一般是基2型的，即要求被变换的数组长度必须是2的m幂次方，
 *     这种要求过于苛刻，当然相比于按照定义进行计算来说，速度是很快的。此外，
 *     还有基4的算法，以及混合基算法等，但都对数组长度N有严格的限制。
 *     所以想自己开发一个适合任意N的FFT算法，还是比较难的，目前还是调用FFTW库暂时凑合着用吧。
 *
 * 参数1：in            输入的一维复数数组
 * 参数2：n             输入/出的一维复数数组的长度
 * 参数3：line_width    数组下标的间隔(默认为1)，对于行变换等于1，对于列变换等于一行的宽度
 * 参数4：is_inv        是否是逆变换(默认不是)
 *
 * 过客 & [email protected] & 2016.01.25
 */
int myfft_c2c_1d_base2(my_complex * in, int n, int line_width/*=1*/, int is_inv/*=0*/)
{
	int ttt = n;
	int L = 1; //蝶形运算的层数
	while(ttt = ttt >> 1){L++;}
	
	my_complex * X = in;

	int N = n;
	int len = 1 << L; //将输入的一维数组对齐为 N=2^L
	if(n * 2 == len) //刚好是2的幂
	{
		L -= 1;
	}else if(n < len) //说明n不是2的幂
	{
//		printf("Erorr: n is not 2^m format.\n"); //非基2算法还有待开发
//		return 0;

		N = len;
		X = new my_complex[N]; //扩充数组大小
		int aaa = sizeof(my_complex);
		memset(X, 0, sizeof(my_complex) * N); //全部初始化为0
		memcpy(X, in, sizeof(my_complex) * n); //复制数据
	}

	//--------数组倒位序 二进制(n0n1n2) => (n2n0n1)-------------------
	//例如： 3的二进制为 011，对应的倒位序为 110，即为6
	my_complex * XX = new my_complex[N];
	for(int i = 0; i < N; i++)
	{
		int p = 0;
		for(int f = 0; f < L; f++)
		{
			if(i & (1 << f))
			{
				p += 1 << (L - f - 1);
			}
		}
		XX[i] = X[p];
	}
	memcpy(X, XX, sizeof(my_complex) * N); //复制数据
	delete [] XX; XX = NULL;

	//---------旋转因子-------------------
	my_complex * W = new my_complex[N / 2];
	memset(W, 0, sizeof(my_complex) * N / 2); //全部初始化为0
	for(int i = 0; i < N / 2; i++)
	{
		W[i] = my_complex(cos(-2.0 * PI * i / N), sin(-2.0 * PI * i / N));
	}

	//---------FFT算法(基2)----------------
	for(int f = 0; f < L; f++) //蝶形运算层数
	{
		int G = 1 << (L - f);
		int num = 1 << f;

		for(int u = 0; u < num; u++) //每组的元素个数
		{
			for(int g = 0; g < G; g += 2) //每层的组数
			{
				my_complex X1 = X[g * num + u];
				my_complex X2 = X[(g + 1) * num + u];

				X[g * num + u]       = X1 + W[u * (1 << (L - f - 1))] * X2; //蝶形运算
				X[(g + 1) * num + u] = X1 - W[u * (1 << (L - f - 1))] * X2; //蝶形运算
			}
		}
	}

	if(X != NULL && X != in) //说明另外申请了内存空间
	{
		memcpy(in, X, sizeof(my_complex) * n);
		if(X){delete [] X; X = NULL;}
	}
	if(W != NULL){delete [] W; W = NULL;}

	return 1;
}


int print_complex_array_1d(my_complex * in, int n)
{
	for(int i = 0; i < n; i++)
	{
		printf("%d:%f+i%f ", i, in[i].r, in[i].i);
	}
	printf("\n");

	return 1;
}


int print_complex_array_2d(my_complex * in, int m, int n)
{
	for(int y = 0; y < n; y++)
	{
		for(int x = 0; x < m; x++)
		{
			printf("%d_%d:%f+i%f ", y, x, (*(in + y * m + x)).r, (*(in + y * m + x)).i);
		}
		printf("\n");
	}
	printf("\n");

	return 1;
}

/*
 * main.cpp
 */

#include 
#include 
#include "myfft.h"


int main(int argc, char * argv[]) //DFT测试 一维
{
	int n = 8;
	int n1 = n;
	int n2 = n;
	my_complex * in = new my_complex[n1];
	my_complex * out = new my_complex[n2];

	double data[] = {4, 3, 2, 6, 7, 8, 9, 0};

	for(int i = 0; i < n; i++)
	{
		in[i].r = data[i]; in[i].i = 0;
		out[i].r = 0; out[i].i = 0;
	}

	print_complex_array_1d(in, n1);

	//----------正变换----------------------
	myfft_by_define_c2c_1d(in, n1, out, n2, 1, 0); //按照定义进行一维复数离散傅里叶变换

	print_complex_array_1d(out, n2);
	
	//----------逆变换----------------------
	memset(in, 0, sizeof(my_complex) * n);

	myfft_by_define_c2c_1d(out, n2, in, n1, 1, 1); //按照定义进行一维复数离散傅里叶变换

	print_complex_array_1d(in, n1);

	if(in){delete [] in; in = NULL;}
	if(out){delete [] out; out = NULL;}

	system("pause");

	return 0;
}
/*
0:4.000000+i0.000000 1:3.000000+i0.000000 2:2.000000+i0.000000 3:6.000000+i0.000000 4:7.000000+i0.000000 5:8.000000+i0.000000 6:9.000000+i0.000000 7:0.000000+i0.000000
0:39.000000+i0.000000 1:-10.778175+i6.292892 2:0.000001+i-5.000001 3:4.778176+i-7.707106 4:5.000000+i0.000001 5:4.778172+i7.707108 6:-0.000002+i4.999998 7:-10.778169+i-6.292899
0:4.000000+i-0.000001 1:3.000000+i-0.000001 2:2.000000+i-0.000000 3:6.000000+i-0.000000 4:7.000000+i0.000000 5:8.000000+i0.000000 6:9.000000+i0.000001 7:0.000000+i0.000001
请按任意键继续. . .
*/


int main2(int argc, char * argv[]) //DFT测试 二维
{
	int m = 3;
	int n = 3;
	my_complex * in = new my_complex[m * n];

	in[0] = my_complex(0, 0); in[1] = my_complex(2, 0); in[2] = my_complex(4, 0);
	in[3] = my_complex(6, 0); in[4] = my_complex(1, 0); in[5] = my_complex(3, 0);
	in[6] = my_complex(5, 0); in[7] = my_complex(7, 0); in[8] = my_complex(4, 0);

	print_complex_array_2d(in, m, n);

	//----------正变换----------------------
	myfft_by_define_c2c_2d(in, m, n, 0); //按照定义进行二维复数离散傅里叶变换
	
	print_complex_array_2d(in, m, n);
	
	//----------逆变换----------------------
	myfft_by_define_c2c_2d(in, m, n, 1); //按照定义进行二维复数离散傅里叶变换
	
	print_complex_array_2d(in, m, n);

	if(in){delete [] in; in = NULL;}

	system("pause");

	return 0;
}
/*
0_0:0.000000+i0.000000 0_1:2.000000+i0.000000 0_2:4.000000+i0.000000
1_0:6.000000+i0.000000 1_1:1.000000+i0.000000 1_2:3.000000+i0.000000
2_0:5.000000+i0.000000 2_1:7.000000+i0.000000 2_2:4.000000+i0.000000

0_0:32.000000+i0.000000 0_1:0.500000+i0.866025 0_2:0.500001+i-0.866027
1_0:-7.000001+i5.196152 1_1:-1.000000+i-1.732051 1_2:-8.499999+i-6.062178
2_0:-6.999999+i-5.196154 2_1:-8.500001+i6.062177 2_2:-1.000000+i1.732051

0_0:0.000000+i-0.000000 0_1:2.000000+i-0.000000 0_2:4.000000+i-0.000000
1_0:6.000000+i-0.000000 1_1:1.000000+i-0.000000 1_2:3.000000+i0.000000
2_0:5.000000+i-0.000000 2_1:7.000000+i0.000000 2_2:4.000000+i0.000001

请按任意键继续. . .
*/


int main3(int argc, char * argv[]) //FFT测试 一维(基2)
{
	int n = 8;
	my_complex * in = new my_complex[n];
	double data[] = {4, 3, 2, 6, 7, 8, 9, 0};

	for(int i = 0; i < n; i++)
	{
		in[i].r = data[i];
		in[i].i = 0;
	}

	print_complex_array_1d(in, n);

	//----------正变换----------------------
	myfft_c2c_1d_base2(in, n, 1, 0); //进行一维复数离散快速傅里叶变换(基2)

	print_complex_array_1d(in, n);

	if(in){delete [] in; in = NULL;}

	system("pause");

	return 0;
}
/*
0:4.000000+i0.000000 1:3.000000+i0.000000 2:2.000000+i0.000000 3:6.000000+i0.000000 4:7.000000+i0.000000 5:8.000000+i0.000000 6:9.000000+i0.000000 7:0.000000+i0.000000
0:39.000000+i0.000000 1:-10.778175+i6.292893 2:0.000000+i-5.000000 3:4.778175+i-7.707106 4:5.000000+i0.000000 5:4.778174+i7.707107 6:-0.000000+i5.000000 7:-10.778175+i-6.292894
请按任意键继续. . .
*/