Diff: fft.cpp

Revision:

0:b771a5301e43

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fft.cpp	Thu Mar 18 15:15:33 2010 +0000
@@ -0,0 +1,161 @@
+/*
+ * This is not my code and I do not take credit for it.
+ * http://www.mit.edu/~emin/source_code/fft/index.html
+ */
+
+#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 fft(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] */
+}
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