#define N 1000
/*定义复数类型*/
typedef struct{
double real;
double img;
}complex;
complex x[N], *W; /*输入序列,变换核*/
int size_x=0; /*输入序列的大小，在本程序中仅限2的次幂*/
double PI; /*圆周率*/
void fft(); /*快速傅里叶变换*/
void initW(); /*初始化变换核*/
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 output();
int main(){
int i; /*输出结果*/
system(\"cls\");
PI=atan(1)*4;
printf(\"Please input the size of x:\\n\");
scanf(\"%d\
printf(\"Please input the data in x[N]:\\n\");
for(i=0;iscanf(\"%lf%lf\initW();
fft();
output();
return 0;
}
/*快速傅里叶变换*/
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<for(j=0;jfor(k=0;kmul(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;
}
}
}
}
/*初始化变换核*/
void initW(){
int i;
W=(complex *)malloc(sizeof(complex) * size_x);
for(i=0;iW[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;ik=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;
}
}
}
/*输出傅里叶变换的结果*/
void output(){
int i;
printf(\"The result are as follows\\n\");
for(i=0;iprintf(\"%.4f\if(x[i].img>=0.0001)printf(\"+%.4fj\\n\
else if(fabs(x[i].img)<0.0001)printf(\"\\n\");
else printf(\"%.4fj\\n\
}
}
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;
}
