/*时间抽选基2FFT及IFFT算法C语言实现*/

/*Author :Junyi Sun*/

/*Copyright 2004-2005*/

/*Mail:ccnusjy@yahoo.com.cn*/

#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);}