#include "stdafx.h"
#include
#include
#include
#include
#include
#define N 1000
/*定义复数类型*/
typedef struct
{
double real;
double img;
}complex;
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*/
complex x[N], W; /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=atan(1)*4; /*定义圆周率*/
int main()
{
int i, X, Y,flt=0;
int gd=DETECT,gm;
system("cls");
printf("输入正弦频率X:\n");
scanf("%d",&X);
printf("输入采样频率Y(理想情况下应是2的整数次幂):\n");
scanf("%d",&Y);
if(int(Y)==2||int(Y)==4||int(Y)==8||int(Y)==16||int(Y)==32||int(Y)==64||int(Y)==128||int(Y)==256||int(Y)==512||int(Y)==1024)
flt=1;
if(flt==0)
{ printf("注意!输入的Y不是2的整数次幂!\n");
}
printf("输入采样点数size_x:\n");
scanf("%d",&size_x);
for(i=0;i<size_x;i++)
{
x[i].real=sin(2*PI*X*i/Y);
x[i].img=0;
}
initW();
fft();
output();
for(i=0;i<size_x;i++)
{ //求变换后结果的模值，存入复数的实部部分
x[i].real=sqrt(x[i].real*x[i].real+x[i].img*x[i].img);
}
//registerbgidriver(EGAVGA_driver);
initgraph(&gd,&gm,"");
cleardevice();
setcolor(WHITE);
line(400,400,400,50);
line(400,50,395,55);
line(400,50,405,55);
line(200,400,600,400);
line(600,400,595,395);
line(600,400,595,405);
setcolor(WHITE);
for(i=0;i<size_x;i++)
line(i*10+400-size_x*10/2,400,i*10+400-size_x*10/2,400-(int)x[i].real*10);
getch();
closegraph();
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<<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;
}
}
}
}
/*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[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<
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)
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);
}
