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();
}
/*初始化变换核*/
void initw(){
int i;
w=(complex *)malloc(sizeof(complex) * size_x);
for(i=0;i<size_x;i++){
w.real=cos(2*pi/size_x*i);
w.img=-1*sin(2*pi/size_x*i);
}
}
/*变址计算，将x(n)码位倒置*/
void change(){
complex temp;
int i=0,j=0,k=0,t;
for(i=0;i<size_x;i++){
k=i;j=0;
t=(unsigned) (log(size_x)/log(2));
while(t--){
j=j<<1;
j|=(k & 1);
k=k>>1;
}
if(j>i){
temp=x;
x=x[j];
x[j]=temp;
}
}
}
/*输出傅里叶变换的结果*/
void output(){
int i;
printf("the result are as follows\n");
for(i=0;i<size_x;i++){
printf("%.4f",x.real);
if(x.img>=0.0001)printf("+%.4fj\n",x.img);
else if(fabs(x.img)<0.0001)printf("\n");
else printf("%.4fj\n",x.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);
}
比如求fft([1,2j,3,4j])
运行过程：
please input the size of x:
4
please input the data in x[n]:
1 0
0 2
3 0
0 4
