#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
/*
利用傅里叶变换的算法计算复数问题
/
#define PI 3.14159265
#define N 4095 //采样256次
/**定义结构体****/
typedef struct
{
double
real;/*实部*/
double
img;/*虚部*/
}complex;
/*输出序列的值*/
complex x[N * 2], W;
/***建立运算类测试类***/
class test {
public:
void add(complex a, complex b, complex *c);
void sub(complex a, complex b, complex *c);
void mul(complex a, complex b, complex *c);
void divi(complex a, complex b, complex *c);
void initW(int size);
void changex(int size);
void fftx();
void output();
};
void test:: add(complex a, complex b, complex *c) // 复数加运算
{
c->real = a.real + b.real;
c->img = a.img + b.img;
}
void test:: sub(complex a, complex b, complex *c) // 复数减运算
{
c->real = a.real - b.real;
c->img = a.img - b.img;
}
void test:: mul(complex a, complex b, complex *c) //复数乘运算
{
c->real = a.real*b.real - a.img*b.img;
c->img = a.real*b.img + a.img*b.real;
}
void test::divi(complex a, complex b, complex *c) // 复数除运算
{
c->real = (a.real*b.real + a.img*b.img) / (b.real*b.real + b.img*b.img);
c->img = (a.img*b.real - a.real*b.img) / (b.real*b.real + b.img*b.img);
}
/***欧拉公式运算****/
void test:: initW(int size)
{
int i;
W = (complex*)malloc(sizeof(complex)* size); //分配内存空间
for
(i = 0; i<size; i++)
{
W[i].real = cos(2 * PI / size * i);
W[i].img = -1 * sin(2 * PI / size * i);
}
}
/**变址运算**/
void test:: changex(int size)
{
complex temp;
unsigned int i = 0, j = 0, k = 0;
double t;
for(i = 0; i<size; i++)
{
k = i; j = 0;
t = (log(size) / log(2));
while((t--)>0)
{
j = j << 1;
j |= (k & 1);
k = k >> 1;
}
if(j>i)
{
temp = x[i];
x[i] = x[j];
x[j] = temp;
}
}
}
void test:: fftx() //快速傅里叶函数
{
long int i = 0, j = 0, k = 0, l = 0;
complex up, down, product;
changex(N);
for(i = 0; i<log(N) / log(2); i++) /*一级蝶形运算*/
{
l = 1 << i;
for (j = 0; j < N; j += 2 * l) /*一组蝶形运算*/
{
for (k = 0; k < l; k++) /*一个蝶形运算*/
{
mul(x[j + k + l], W[N*k / 2 / l], &product);
add(x[j + k], product, &up);
sub(x[j + k], product, &down);
x[j + k] = up;
x[j + k + l] = down;
}
}
}
}
void test::output() /*输出x结果*/
{
int i;
cout << "\nx傅里叶变换结果\n" << endl;
for(i = 0; i
{
if(i % 4 == 0 && i != 0)
cout
cout
if(x[i].img >= 0.0001)
cout<<x[i].img<<endl;
else
if (fabs(x[i].img)<0.0001)
cout<<"+0.0000j "<<endl;
else
cout<< x[i].img<<endl;
}
cout<<"\n"<<endl;
}
int main()
{
test si;
clock_t
start = clock();
double duration;
/*对x进行傅里叶变换*/
int i, j = 0, t = 0;
double data[N * 2] = { 0 };
double result[N * 2] = { 0 };
float tx = 0;
for(t = 0; t < N; t++)
{
data[t] = 5 + 7 * cos(30 * PI / 128 * t - 30 * PI / 180) + 3 * cos(80 * PI / 128 * t - 90 * PI / 180);
}
for(i = 0; i<N; i++) //求出x的256个采样点的值 下一步傅里叶变化
{
x[i].real = data[i];
x[i].img = 0;
}
si.initW(N);
si.fftx();
cout << "输出信号的模";
cout << endl;
for(i = 0; i < N; i++)
{
result[i] = sqrt(x[i].real*x[i].real + x[i].img*x[i].img);
if(i % 4 == 0)
cout << endl;
cout << setprecision(2) << result[i] / N * 2 << " ";
}
clock_t
end = clock();
cout << "所用的时间： ";
duration = (double)(end - start) / CLOCKS_PER_SEC;
cout << duration << "ms";
cout << endl;
return 0;
}
