#include %26lt;stdio.h%26gt;
#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",%26amp;data[0],%26amp;data[1],%26amp;data[2],%26amp;data[3],...
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],z...
printf("1\t\t%.9f\t\t%.9f\n",output[1],o...
printf("2\t\t%.9f\t\t%.9f\n",output[2],o...
printf("3\t\t%.9f\t\t%.9f\n",output[3],o...
printf("4\t\t%.9f\t\t%.9f\n",output[4],o...
printf("5\t\t%.9f\t\t%.9f\n",output[5],o...
printf("6\t\t%.9f\t\t%.9f\n",output[6],o...
printf("7\t\t%.9f\t\t%.9f\n",output[7],o...
printf("8\t\t%.9f\t\t%.9f\n",output[8],z...
printf("9\t\t%.9f\t\t%.9f\n",output[7],-...
printf("10\t\t%.9f\t\t%.9f\n",output[6],...
printf("11\t\t%.9f\t\t%.9f\n",output[5],...
printf("12\t\t%.9f\t\t%.9f\n",output[4],...
printf("13\t\t%.9f\t\t%.9f\n",output[3],...
printf("14\t\t%.9f\t\t%.9f\n",output[2],...
printf("15\t\t%.9f\t\t%.9f\n",output[1],...
}
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