fft.c

fft和ifft的c程序代码

#include <stdio.h>
#define SIN_2PI_16 0.38268343236508978
#define SIN_4PI_16 0.707106781186547460
#define SIN_6PI_16 0.923879532511286740
#define C_P_S_2PI_16 1.30656296487637660
#define C_M_S_2PI_16 0.54119610014619690
#define C_P_S_6PI_16 1.3065629648763766
#define C_M_S_6PI_16 -0.54119610014619690

/* INPUT: float input[16], float output[16] */
/* OUTPUT: none */
/* EFFECTS:  Places the 16 point fft of input in output in a strange */
/* order using 10 real multiplies and 79 real adds. */
/* Re{F[0]}= out0 */
/* Im{F[0]}= 0 */
/* Re{F[1]}= out8 */
/* Im{F[1]}= out12 */
/* Re{F[2]}= out4 */
/* Im{F[2]}= -out6 */
/* Re{F[3]}= out11 */
/* Im{F[3]}= -out15 */
/* Re{F[4]}= out2 */
/* Im{F[4]}= -out3 */
/* Re{F[5]}= out10 */
/* Im{F[5]}= out14 */
/* Re{F[6]}= out5 */
/* Im{F[6]}= -out7 */
/* Re{F[7]}= out9 */
/* Im{F[7]}= -out13 */
/* Re{F[8]}= out1 */
/* Im{F[8]}=0 */
/* F[9] through F[15] can be found by using the formula */
/* Re{F[n]}=Re{F[(16-n)mod16]} and Im{F[n]}= -Im{F[(16-n)mod16]} */

/* Note using temporary variables to store intermediate computations */
/* in the butterflies might speed things up.  When the current version */
/* needs to compute a=a+b, and b=a-b, I do a=a+b followed by b=a-b-b.  */
/* So practically everything is done in place, but the number of adds */
/* can be reduced by doinc c=a+b followed by b=a-b. */

/* The algorithm behind this program is to find F[2k] and F[4k+1] */
/* seperately.  To find F[2k] we take the 8 point Real FFT of x[n]+x[n+8] */
/* for n from 0 to 7.  To find F[4k+1] we take the 4 point Complex FFT of */
/* exp(-2*pi*j*n/16)*{x[n] - x[n+8] + j(x[n+12]-x[n+4])} for n from 0 to 3.*/

void R16SRFFT(float input[16],float output[16] ) {
  float temp, out0, out1, out2, out3, out4, out5, out6, out7, out8;
  float out9,out10,out11,out12,out13,out14,out15;

  out0=input[0]+input[8]; /* output[0 through 7] is the data that we */
  out1=input[1]+input[9]; /* take the 8 point real FFT of. */
  out2=input[2]+input[10];
  out3=input[3]+input[11];
  out4=input[4]+input[12];
  out5=input[5]+input[13];
  out6=input[6]+input[14];
  out7=input[7]+input[15];



  out8=input[0]-input[8];   /* inputs 8,9,10,11 are */
  out9=input[1]-input[9];   /* the Real part of the */
  out10=input[2]-input[10]; /* 4 point Complex FFT inputs.*/
  out11=input[3]-input[11]; 
  out12=input[12]-input[4]; /* outputs 12,13,14,15 are */
  out13=input[13]-input[5]; /* the Imaginary pars of  */
  out14=input[14]-input[6]; /* the 4 point Complex FFT inputs.*/
  out15=input[15]-input[7];

  /*First we do the "twiddle factor" multiplies for the 4 point CFFT */
  /*Note that we use the following handy trick for doing a complex */
  /*multiply:  (e+jf)=(a+jb)*(c+jd) */
  /*   e=(a-b)*d + a*(c-d)   and    f=(a-b)*d + b*(c+d)  */

  /* C_M_S_2PI/16=cos(2pi/16)-sin(2pi/16) when replaced by macroexpansion */
  /* C_P_S_2PI/16=cos(2pi/16)+sin(2pi/16) when replaced by macroexpansion */
  /* (SIN_2PI_16)=sin(2pi/16) when replaced by macroexpansion */
  temp=(out13-out9)*(SIN_2PI_16); 
  out9=out9*(C_P_S_2PI_16)+temp; 
  out13=out13*(C_M_S_2PI_16)+temp;
  
  out14*=(SIN_4PI_16);
  out10*=(SIN_4PI_16);
  out14=out14-out10;
  out10=out14+out10+out10;
  
  temp=(out15-out11)*(SIN_6PI_16);
  out11=out11*(C_P_S_6PI_16)+temp;
  out15=out15*(C_M_S_6PI_16)+temp;

  /* The following are the first set of two point butterfiles */
  /* for the 4 point CFFT */

  out8+=out10;
  out10=out8-out10-out10;

  out12+=out14;
  out14=out12-out14-out14;

  out9+=out11;
  out11=out9-out11-out11;

  out13+=out15;
  out15=out13-out15-out15;

  /*The followin are the final set of two point butterflies */
  output[1]=out8+out9;
  output[7]=out8-out9;

  output[9]=out12+out13;
  output[15]=out13-out12;
  
  output[5]=out10+out15;        /* implicit multiplies by */
  output[13]=out14-out11;        /* a twiddle factor of -j */                            
  output[3]=out10-out15;  /* implicit multiplies by */
  output[11]=-out14-out11;  /* a twiddle factor of -j */

  
  /* What follows is the 8-point FFT of points output[0-7] */
  /* This 8-point FFT is basically a Decimation in Frequency FFT */
  /* where we take advantage of the fact that the initial data is real*/

  /* First set of 2-point butterflies */
    
  out0=out0+out4;
  out4=out0-out4-out4;
  out1=out1+out5;
  out5=out1-out5-out5;
  out2+=out6;
  out6=out2-out6-out6;
  out3+=out7;
  out7=out3-out7-out7;

  /* Computations to find X[0], X[4], X[6] */
  
  output[0]=out0+out2;
  output[4]=out0-out2;
  out1+=out3;
  output[12]=out3+out3-out1;

  output[0]+=out1;  /* Real Part of X[0] */
  output[8]=output[0]-out1-out1; /*Real Part of X[4] */
  /* out2 = Real Part of X[6] */
  /* out3 = Imag Part of X[6] */
  
  /* Computations to find X[5], X[7] */

  out5*=SIN_4PI_16;
  out7*=SIN_4PI_16;
  out5=out5-out7;
  out7=out5+out7+out7;

  output[14]=out6-out7; /* Imag Part of X[5] */
  output[2]=out5+out4; /* Real Part of X[7] */
  output[6]=out4-out5; /*Real Part of X[5] */
  output[10]=-out7-out6; /* Imag Part of X[7] */

}

void main() {
  float data[16];
  float output[16];
  float zero=0;

  printf("\ntype 16 point input vector\n");
  scanf("%f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f",&data[0],&data[1],&data[2],&data[3],&data[4],&data[5],&data[6],&data[7],&data[8],&data[9],&data[10],&data[11],&data[12],&data[13],&data[14],&data[15]);
  
  R16SRFFT(data,output);
  printf("\nresult is:\n");
  printf("k,\t\tReal Part\t\tImaginary Part\n");
    printf("0\t\t%.9f\t\t%.9f\n",output[0],zero);
  printf("1\t\t%.9f\t\t%.9f\n",output[1],output[9]);
  printf("2\t\t%.9f\t\t%.9f\n",output[2],output[10]);
  printf("3\t\t%.9f\t\t%.9f\n",output[3],output[11]);
  printf("4\t\t%.9f\t\t%.9f\n",output[4],output[12]);
  printf("5\t\t%.9f\t\t%.9f\n",output[5],output[13]);
  printf("6\t\t%.9f\t\t%.9f\n",output[6],output[14]);
  printf("7\t\t%.9f\t\t%.9f\n",output[7],output[15]);
  printf("8\t\t%.9f\t\t%.9f\n",output[8],zero);
  printf("9\t\t%.9f\t\t%.9f\n",output[7],-output[15]);
  printf("10\t\t%.9f\t\t%.9f\n",output[6],-output[14]);
  printf("11\t\t%.9f\t\t%.9f\n",output[5],-output[13]);
  printf("12\t\t%.9f\t\t%.9f\n",output[4],-output[12]);
  printf("13\t\t%.9f\t\t%.9f\n",output[3],-output[11]);
  printf("14\t\t%.9f\t\t%.9f\n",output[2],-output[9]);
  printf("15\t\t%.9f\t\t%.9f\n",output[1],-output[8]);
}