#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#define N 1000
typedef struct
{
double real;
double img;
}complex;
void fft();
void initw();
void change();
void add(complex,complex,complex *);
void mul(complex,complex,complex *);
void sub(complex,complex,complex *);
void divi(complex,complex,complex *);
void output();
complex x[N],*W;
int size_x=0;
double PI=3.1415926;
int main()
{
int i,method;
system("cls");
printf("请输入序列的点数:\n");
scanf("%d",&size_x);
printf("请输入序列中每一点数据的实部与虚部:(such as:1 2)\n");
for(i=0;i<size_x;i++)
{
printf("x[%d]:",i);
scanf("%lf %lf",&x[i].real,&x[i].img);
}
initw();
fft();
output();
return 0;
}
void fft()
{
int i=0,j=0,k=0,l=0;
complex up,down,product;
change();
for(i=0;i<log(size_x)/log(2);i++)
{
l=1<<i;
for(j=0;j<size_x;j+=2*l)
{
for(k=0;k<l;k++)
{
mul(x[j+k+l],W[size_x*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 initw()
{
int i;
W=(complex *)malloc(sizeof(complex)*size_x);
for(i=0;i<size_x;i++)
{
W[i].real=cos(2*PI/size_x*i);
W[i].img=-sin(2*PI/size_x*i);
}
}
void change()
{
complex temp;
unsigned short i=0,j=0,k=0;
double t;
for(i=0;i<size_x;i++)
{
k=i;j=0;
t=(log(size_x)/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 output()
{
int i;
printf("结果如下：\n");
for(i=0;i<size_x;i++)
{
printf("%.4f",x[i].real);
if(x[i].img>=0.0001)
printf("+%.4fj\n",x[i].img);
else if(fabs(x[i].img)<0.0001)
printf("\n");
else
printf("%.4fj\n",x[i].img);
}
}
void add(complex a,complex b,complex *c)
{
c->real=a.real+b.real;
c->img=a.img+b.img;
}
void mul(complex a,complex b,complex *c)
{
c->real=a.real*b.real-a.img*b.img;
c->img=a.real*b.img+a.img*b.real;
}
void sub(complex a,complex b,complex *c)
{
c->real=a.real-b.real;
c->img=a.img-b.img;
}
void divi(complex a,complex b,complex *c)
{
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);
}
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