fft.rar_C++fft运算pudn_C++实现fft函数

#include <stdio.h> #include <math.h> #include <stdlib.h> #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 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(); int main(){ int i,method; /*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<size_x;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(); //scanf("%d",i);scanf("%d",i); 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; } } } } /*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<size_x;j+= 2*l ){ /*一组蝶形运算*/ 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[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<size_x;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<size_x;i++) { printf("%.4f",x[i].real); if(x[i].img>=0.0001)printf("+%.4fi\n",x[i].img); else if(fabs(x[i].img)<0.0001)printf("\n"); else printf("%.4fi\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); }