时间抽选基2FFT及IFFT算法C语言实现

/*时间抽选基2FFT及IFFT算法C语言实现*/
/*Author :Junyi Sun*/
/*Copyright 2004-2005*/
/*Mail:[email protected]*/
#include
#include
#include
#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*/

int main(){
 int i,method;
 void fft();    /*快速傅里叶变换*/
 void ifft();
 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 divi(complex ,complex ,complex *);/*复数除法*/
 void output();                            /*输出结果*/
 system("cls");
 PI=atan(1)*4;
 printf("Please input the size of x:/n");
 scanf("%d",&size_x);
 printf("Please input the data in x[N]:/n");
 for(i=0;i  scanf("%lf%lf",&x[i].real,&x[i].img);
 initW();
 printf("Use FFT(0) or IFFT(1)?/n");
 scanf("%d",&method);
 if(method==0)
  fft();
 else
  ifft();
 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;j   for(k=0;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;
   }
  }
 }
}

/*快速傅里叶逆变换*/
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   for(k=0;k    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  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  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;
  }
 }
}

/*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  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);
}