/************FFT***********/
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#define N 1000
typedef struct
{
double real;/*实部*/
double img;/*虚部*/
}complex;
void fft(); /*快速傅里叶变换*/
void ifft(); /*快速傅里叶逆变换*/
void initW(); /*初始化变化核*/
void change(); /*变址*/
void add(complex ,complex ,complex *); /*复数加法*/
void mul(complex ,complex ,complex *); /*复数乘法*/
void sub(complex ,complex ,complex *); /*复数减法*/
void divi(complex ,complex ,complex *); /*复数除法*/
void output(); /*输出结果*/
complex x[N], *W;/*输出序列的值*/
int size_x=0;/*输入序列的长度，只限2的N次方*/
double PI;
int main()
{
int i,method;
system("cls");
PI=atan(1)*4;/*pi等于4乘以1.0的正切值*/
printf("Please input the size of x :\n");
/*输入序列的长度*/
scanf("%d",&size_x);
printf("Please input the data in x[N](complex):(such as:5 6)\n");
/*输入序列对应的值*/
for(i=0;i<size_x;i++)
scanf("%lf %lf",&x[i].real,&x[i].img);
initW();
/*选择FFT或逆FFT运算*/
printf("Use FFT(0) or IFFT(1)?\n");
scanf("%d",&method);
if(method==0)
fft();
else
ifft();
output();
system("pause");
return 0;
}
/*进行基-2 FFT运算*/
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++) /*一级蝶形运算*/
{
l=1<<i;
for(j=0;j<size_x;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[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 ifft()
{
int i=0,j=0,k=0,l=size_x;
complex up,down;
for(i=0;i< (int)( log(size_x)/log(2) );i++) /*一级蝶形运算*/
{
l/=2;
for(j=0;j<size_x;j+= 2*l ) /*一组蝶形运算*/
{
for(k=0;k<l;k++) /*一个蝶形运算*/
{
add(x[j+k],x[j+k+l],&up);
up.real/=2;up.img/=2;
sub(x[j+k],x[j+k+l],&down);
down.real/=2;down.img/=2;
divi(down,W[size_x*k/2/l],&down);
x[j+k]=up;
x[j+k+l]=down;
}
}
}
change();
}
/*初始化变化核*/
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=-1*sin(2*PI/size_x*i);
}
}
/*变址计算，将x(n)码位倒置*/
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() /*输出结果*/
{
int i;
printf("The result are as follows\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);
}
