fft_dit_general.c

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/***********************************
// DIT radix-4  FFT  complex 
//
// 1. Maximium points are 2048 because that 
//    function mylog2(int N) has the limit of maximal points
//
// 2. The last stage is 2 DFT ( for 8, 32, 128, 512, 2048...)
// or 4 DFT ( for 4, 16, 64, 256, 1024 ...).
//
//
// 24 juillet 2007
// purcharse*gmail.com
************************************/

#include <math.h>
#include <stdio.h>
#include <stdlib.h>

typedef double real64;      /* floating point */
typedef float  real32;    /* 32 bit fixed point */

struct complex
{ 
  real32 real;
  real32 imag;
} complex ;

static struct complex multicomplex(struct complex,struct complex);
static int mylog2(int); 

static void RunFFT(struct complex *,int);
static void DFT_2(struct complex *,struct complex *);
static void DFT_4(struct complex *,struct complex *,struct complex *,struct complex *);

static void RunFFT(struct complex *, int);
static void RunIFFT(struct complex *,int);

static void BitReverse(struct complex *, int);
static void FFT_R4(struct complex *, int, int);
static void FFT_L2(struct complex *, int);

struct  complex s[257];
int   Num = 16;
const float PI=3.1415926535898;

main()
{
	int i;

	/* rectangle */
      /*
      for(i=0;i<Num+1;i++)
      {
          s[i].real=0;
          s[i].imag=0;
      }

	s[0].real = 10;
	s[0].imag = 10;
	*/

	/*  sinus*/
	
      for(i=0;i<Num+1;i++)
      {
          s[i].real=sin(PI*i/Num);
          s[i].imag=cos(PI*i/Num);
      } 
	
	/*  */
	/*
      for(i=0;i<Num+1;i++)
      {
          s[i].real=0;
          s[i].imag=0;
      }
      for(i=Num*3/8;i<Num/2;i++)
      {
          s[i].real=(i-Num*3/8);
          s[i].imag=0;
      }
      for(i=Num/2;i<Num*5/8;i++)
      {
          s[i].real=(Num*5/8-i);
          s[i].imag=0;
      }       */   

	printf("*********** Donnees *****************\n");
	for(i=0;i<Num;i++)
	{
		printf("%.4f\t\t",s[i].real);
		printf("%.4f\n",s[i].imag);
	}
	
	RunFFT(s, Num);
	printf("*********** FFT *****************\n");
	for(i=0;i<Num;i++)
	{
		printf("%.4f\t\t",s[i].real);
		printf("%.4f\n",s[i].imag);
	}
	RunIFFT(s, Num);
	printf("*********** IFFT *****************\n");
	for(i=0;i<Num;i++)
	{
		printf("%.4f\t\t",s[i].real);
		printf("%.4f\n",s[i].imag);
	}
}
/***************** functions ********************/

static struct complex multicomplex(struct complex b1,struct complex b2)  /* multiplication of complex */
{
struct complex b3;
b3.real=b1.real*b2.real-b1.imag*b2.imag;
b3.imag=b1.real*b2.imag+b1.imag*b2.real;
return(b3);
}

static int mylog2(int N) 	/* Max(N) = 4098 */
{
  int k=0;
  
  if (N>>12) { k+=12; N>>=12; }
  if (N>>8) { k+=8; N>>=8; }
  if (N>>4) { k+=4; N>>=4; }
  if (N>>2) { k+=2; N>>=2; }
  if (N>>1) { k+=1; N>>=1; }
  return k ;
}


static void BitReverse(struct complex *xin, int N)
{
	int LH, i, j, k;
	struct complex tmp;

			LH=N/2;    
			j = N/2;

			for( i = 1; i <= (N -2); i++)
			{
				if(i < j)
				{
					tmp = xin[j];
					xin[j] = xin[i];
					xin[i] = tmp;
				}
			k = LH;
				while(j >= k)
				{
					j = j-k;
					k = k/2;
				}

			j = j + k;

			}

}

static void DFT_2(struct complex *b1,struct complex *b2)
{
struct complex tmp;
  tmp = *b1;

  (*b1).real = (*b1).real + (*b2).real;
  (*b1).imag = (*b1).imag + (*b2).imag;

  (*b2).real = tmp.real - (*b2).real;
  (*b2).imag = tmp.imag - (*b2).imag;	
}

static void DFT_4(struct complex* b0, struct complex* b1, struct complex* b2,struct complex* b3)
{
  /*variables locales*/
  struct complex temp[4];
  
  /*calcul x1*/
  temp[0].real=(*b0).real+(*b1).real;		
  temp[0].imag=(*b0).imag+(*b1).imag;

  /*calcul x2*/
  temp[1].real=(*b0).real-(*b1).real;		
  temp[1].imag=(*b0).imag-(*b1).imag;

  /*calcul x3*/
  temp[2].real=(*b2).real+(*b3).real;	
  temp[2].imag=(*b2).imag+(*b3).imag;

  /*calcul x4 + multiplication with -j*/
  temp[3].imag=(*b3).real-(*b2).real;		
  temp[3].real=(*b2).imag-(*b3).imag; 

  /*the last stage*/
  (*b0).real=temp[0].real+temp[2].real;
  (*b0).imag=temp[0].imag+temp[2].imag;
  
  (*b1).real=temp[1].real+temp[3].real;     
  (*b1).imag=temp[1].imag+temp[3].imag; 
  
  (*b2).real=temp[0].real-temp[2].real;     
  (*b2).imag=temp[0].imag-temp[2].imag;
  
  (*b3).real=temp[1].real-temp[3].real; 
  (*b3).imag=temp[1].imag-temp[3].imag;
}

static void FFT_R4(struct complex *xin, int N, int m)
{
		int  i, L, j;
		double  ps1, ps2, ps3, p ;
		int le,B;
		struct complex w[4];

		for( L = 1; L <= m; L++)
		{
			le = pow(4 ,L);
			B = le/4;       /*the distance of buttefly*/
		
			p = N/le;

 			for(j = 0; j <= B-1 ; j++)	
  			{
			       //  ps0 = (2*pp/N) * 0 * j;
			       //  w[0].real = cos(ps0);
			       //  w[0].imag = -sin(ps0);
	
				   ps1 = (2*PI/N)*p*2*j;
				   w[1].real = cos(ps1);
				   w[1].imag = -sin(ps1);

				   ps2 = (2*PI/N)*p*1*j;
				   w[2].real = cos(ps2);
				   w[2].imag = -sin(ps2);

				   ps3 = (2*PI/N)*p*3*j;
				   w[3].real = cos(ps3);
				   w[3].imag = -sin(ps3);

				   for(i = j; i <= N-1; i = i + le)	/* controle those same butteflies*/
				     {
						/* multiple with W */
				 //   xin[i] = multicomplex(xin[i], w[0]);
				      xin[i + B] = multicomplex(xin[i + B], w[1]);
				      xin[i + 2*B] = multicomplex(xin[i + 2*B], w[2]);
				      xin[i + 3*B] = multicomplex(xin[i + 3*B], w[3]);
						/* DFT-4 */
				      DFT_4(xin + i, xin + i + B, xin + i + 2*B, xin + i + 3*B);
				     }
  		      }
		/*
		printf("*****N°%d **********\n", L);
		for(i=0;i<Num;i++)
		{
		printf("%.8f\t\t",xin[i].real);
		printf("%.8f\n",xin[i].imag);
		}
		*/
		}
	
}//fin du FFT_R4

static void FFT_L2(struct complex *xin, int N)
{				/* For the last stage 2 DFT*/
	int j, B;
	double p, ps ;
	struct complex w;

		B = N/2;   			
		for(j = 0; j <= B - 1; j++)
		{			
			ps = (2*PI/N)*j;
		        w.real = cos(ps);
			w.imag = -sin(ps);

	    	 	/* multiple avec W */
            		 xin[j+ B] = multicomplex(xin[j + B], w);
			 DFT_2(xin + j ,xin + j + B);
		}
				
}//fin du FFT_L2

static void RunFFT(struct complex *xin, int N)
{
	int m, i;
	
	BitReverse(xin, N);
	m = mylog2(N);
	if( (m%2) == 0 )
	{
		/*All the stages are radix 4*/
		FFT_R4(xin, N, m/2);
	}
	else 
	{
		/*the last stage is radix 2*/
		FFT_R4(xin, N, m/2);
		FFT_L2(xin, N);
	}
}

static void RunIFFT(struct complex *xin,int N)
{			/* inverse FFT */
      int i;
    
      for(i=0; i < Num + 1 ; i++)
      { 
	xin[i].imag = -xin[i].imag;
      }
      RunFFT(xin,N);
      for(i = 0; i < Num + 1 ; i++)
      { 
	xin[i].real = xin[i].real/Num;
	xin[i].imag = -xin[i].imag/Num;
      }
}