C语言数据结构算法之实现快速傅立叶变换

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define PI 3.14159265358979323846
 
struct COMPLEX
{
  float re;
  float im;
} cplx , * Hfield , * S , * R , * w;
 
int n , m;
int ln , lm;
 
void initiate ();
void dfft ();
void rdfft ();
void showresult ();
 
void fft (int l , int k);
int reverse (int t , int k);
void W (int l);
int loop (int l);
void conjugate ();
 
void add (struct COMPLEX * x , struct COMPLEX * y , struct COMPLEX * z);
void sub (struct COMPLEX * x , struct COMPLEX * y , struct COMPLEX * z);
void mul (struct COMPLEX * x , struct COMPLEX * y , struct COMPLEX * z);
struct COMPLEX * Hread(int i , int j);
void Hwrite (int i , int j , struct COMPLEX x);
 
void main ()
{
  initiate ();
  printf("\n原始数据:\n");
  showresult();
  getchar ();
  dfft ();
  printf("\n快速复利叶变换后的结果:\n");
  showresult ();
  getchar ();
  rdfft ();
  printf("\n快速复利叶逆变换后的结果:\n");
  showresult ();
  getchar ();
  free (Hfield);
}
 
void initiate ()
{//程序初始化操作，包括分配内存、读入要处理的数据、进行显示等
  FILE * df;
   
  df = fopen ("data.txt" , "r");
  fscanf (df , "%5d" , &n);
  fscanf (df , "%5d" , &m);
  if ((ln = loop (n)) == -1)
  {
    printf (" 列数不是2的整数次幂 ");
    exit (1);
  }
  if ((lm = loop (m)) == -1)
  {
    printf (" 行数不是2的整数次幂 ");
    exit (1);
  }
  Hfield = (struct COMPLEX *) malloc (n * m * sizeof (cplx));
  if (fread (Hfield , sizeof (cplx) , m * n , df) != (unsigned) (m * n))
  {
    if (feof (df)) printf (" Premature end of file ");
    else printf (" File read error ");
  }
  fclose (df);
}
 
void dfft ()
{//进行二维快速复利叶变换
  int i , j; 
  int l , k;
   
  l = n;
  k = ln;
  w = (struct COMPLEX *) calloc (l , sizeof (cplx));
  R = (struct COMPLEX *) calloc (l , sizeof (cplx));
  S = (struct COMPLEX *) calloc (l , sizeof(cplx));
  W (l);
  for ( i = 0 ; i < m ; i++ )
  {//按行进行快速复利叶变换
    for (j = 0 ; j < n ; j++)
    {      
      S[j].re = Hread (i , j)->re;
      S[j].im = Hread (i , j)->im;
    }
    fft(l , k);
    for (j = 0 ; j < n ; j++)
      Hwrite (i , j , R[j]);
  }
  free (R);
  free (S);
  free (w);
   
  l = m;
  k = lm;
  w = (struct COMPLEX *) calloc (l , sizeof (cplx));
  R = (struct COMPLEX *) calloc (l , sizeof (cplx));
  S = (struct COMPLEX *) calloc (l , sizeof (cplx));
  W (l);
  for (i = 0 ; i < n ; i++)
  {//按列进行快速复利叶变换
    for(j = 0 ; j < m ; j++)
    {
      S[j].re = Hread(j , i)->re;
      S[j].im = Hread(j , i)->im;
    }
    fft(l , k);
    for (j = 0 ; j < m ; j++)
      Hwrite (j , i , R[j]);
  }
  free (R);
  free (S);
  free (w);
}
 
void rdfft ()
{
  conjugate ();
  dfft ();
  conjugate ();
}
 
void showresult ()
{
  int i , j;
  for (i = 0 ; i < m ; i++)
  {
    printf ( " \n第%d行\n " , i);
    for (j = 0 ; j < n ; j++)
    {
      if (j % 4 == 0) printf (" \n ");
      printf(" (%5.2f,%5.2fi) " , Hread (i , j)->re , Hread (i , j)->im);
    }
  }
}
 
void fft (int l , int k)
{
  int i , j , s , nv , t;
  float c;
  struct COMPLEX mp , r;
  nv = l;
  c = (float) l;
  c = pow (c , 0.5);
  for (i = 0 ; i < k ; i++)
  {
    for (t = 0 ; t < l ; t += nv)
    {
      for (j = 0 ; j < nv / 2 ; j++)
      {
        s = (t + j) >> (k - i -1);
        s = reverse(s , k);
        r.re = S[t + j].re;
        r.im = S[t + j].im;
        mul (&w[s] , &S[t + j + nv / 2] , &mp);/////////讲解传递结构指针和结构本身的区别
        add (&r , &mp , &S[t + j]);
        sub (&r , &mp , &S[t + j + nv / 2]);        
      }
    }
    nv = nv >> 1;   
  }
 
  for (i = 0 ; i < l ; i++)
  {
    j = reverse(i , k);
    R[j].re = S[i].re / c;
    R[j].im = S[i].im / c;
  }
}
 
int reverse (int t , int k)
{
  int i , x , y;
  y = 0;
  for (i = 0 ; i < k ; i++)
  {
    x = t & 1;
    t = t >> 1;
    y = (y << 1) + x;   
  }
  return y;
}
 
void W (int l)
{
  int i;
  float c , a;
  c = (float) l;
  c = 2 * PI / c;
  for (i = 0 ; i < l ; i++)
  {    
    a = (float) i;
    w[i].re = (float) cos(a * c);
     
    w[i].im = -(float) sin(a * c);
  }
}
 
int loop (int l)
{//检验输入数据是否为2的整数次幂，如果是返回用2进制表示时的位数
  int i , m;
  if (l != 0)
  {
    for (i = 1 ; i < 32 ; i++)
    {
      m = l >> i;
      if (m == 0)
        break;
    }
    if (l == (1 << (i - 1)))
      return i - 1;
  }
  return -1;
}
 
void conjugate ()
{//求复数矩阵的共轭矩阵
  int i , j;
  for (i = 0 ; i < m ; i++)
  {
    for (j = 0 ; j < n ; j++)
    {
      Hread (i , j)->im *= -1;
    }
  }
}
 
struct COMPLEX * Hread (int i , int j)
{//按读矩阵方式返回Hfield中指定位置的指针
  return (Hfield + i * n + j);
}
 
void Hwrite (int i , int j , struct COMPLEX x)
{//按写矩阵方式将复数结构x写到指定的Hfield位置上
  (Hfield + i * n + j)->re = x.re;
  (Hfield + i * n + j)->im = x.im;
}
 
void add (struct COMPLEX * x , struct COMPLEX * y , struct COMPLEX * z)
{//定义复数加法
  z->re = x->re + y->re;
  z->im = x->im + y->im; 
}
 
void sub (struct COMPLEX * x , struct COMPLEX * y , struct COMPLEX * z)
{//定义复数减法
  z->re = x->re - y->re;
  z->im = x->im - y->im;
}
 
void mul (struct COMPLEX * x , struct COMPLEX * y , struct COMPLEX * z)
{//定义复数乘法
  z->re = (x->re) * (y->re) - (x->im) * (y->im);
  z->im = (x->im) * (y->re) + (x->re) * (y->im);
}