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fft.c
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fft.c
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/* Wyznaczenie FFT sygnalu z okienkowaniem 1997 01 17; 1997 10 04 */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "shell.h"
#include "proto.h"
/* Interface dla programu HMPP */
#define DVECTOR() (double *)malloc(Size)
#define SQR(X) (dtmp=(X),dtmp*dtmp)
#define WINDOW1(j,a,b) (1.0-fabs((((j)-1)-(a))*(b))) /* Parzen */
#define WINDOW2(j,a,b) 1.0 /* Square */
#define WINDOW3(j,a,b) (1.0-SQR((((j)-1)-(a))*(b))) /* Welch */
#define STRING 256 /* Maksymalna dlugosc napisow */
#define MAXARGS 30 /* Maksymalna liczba argumentow */
#define PARZEN 1
#define SQARE 2
#define WELCH 3
#define ORGINAL 0
#define RESIDUAL 1
#define YES 1
#define NO 0
#define FREEALL() if(xRe!=NULL) free((void *)xRe); \
if(xIm!=NULL) free((void *)xIm); \
if(yRe!=NULL) free((void *)yRe); \
if(yIm!=NULL) free((void *)yIm)
/* extern float SamplingRate; Czestotliwosc probkowania */
static int fft(int,double *,double *,double *,double *); /* FFT dla dowolnego n */
static int ComputeFFT(int n,float signal[],float ffttab[],int wind,int phase)
{
const unsigned Size=n*sizeof(double);
double *xRe,*xIm=NULL,*yRe=NULL,*yIm=NULL,dtmp,facm,facp,sumw=0.0,w;
int i,j; /* FFT sygnalu + okienkowanie */
if((xRe=DVECTOR())==NULL ||
(xIm=DVECTOR())==NULL ||
(yRe=DVECTOR())==NULL ||
(yIm=DVECTOR())==NULL)
{
FREEALL();
return -1;
}
facm=0.5*(double)(n-1)-0.5;
facp=1.0/(0.5*(double)(n-1)+0.5);
for(i=0 ; i<n ; i++)
{
switch(wind) {
case PARZEN:
w=WINDOW1(i,facm,facp);
break;
case SQARE:
w=WINDOW2(i,facm,facp);
break;
case WELCH:
default:
w=WINDOW3(i,facm,facp);
break;
}
xRe[i]=w*(double)signal[i];
xIm[i]=0.0;
sumw+=SQR(w);
}
if(fft(n,xRe,xIm,yRe,yIm)==-1)
{
FREEALL();
return -1;
}
if(phase==YES)
{
for(i=n/2,j=0 ; i>=0 ; i--,j++)
if(yRe[i]!=0.0 && yIm[i]!=0.0)
ffttab[j]=atan2(yRe[i],yIm[i]);
else
ffttab[i]=0.0;
}
else
for(i=n/2,j=0 ; i>=0 ; i--,j++)
ffttab[j]=sqrt(SQR(yRe[i])+SQR(yIm[i]))/sumw;
FREEALL();
return 0;
}
void SpectrumFFT(char *opt) /* Wyznaczenie FFT sygnalu */
{
char *argv[MAXARGS],filename[STRING]="fftsig.asc";
int opcja,window=WELCH,sig=ORGINAL,phase=NO,i,argc,
itmp,a=0,b=(int)DimBase,n;
float *Tabfft,df;
FILE *stream;
StrToArgv(opt,argv,&argc);
opterr=optind=0; sp=1;
while((opcja=Getopt(argc,argv,"O:w:ropax:y:"))!=EOF)
switch(opcja) {
case 'O':
(void)strcpy(filename,optarg);
break;
case 'x':
a=atoi(optarg);
break;
case 'y':
b=atoi(optarg);
break;
case 'w':
window=atoi(optarg);
break;
case 'o':
sig=ORGINAL;
break;
case 'r':
sig=RESIDUAL;
break;
case 'p':
phase=YES;
break;
case 'a':
phase=NO;
break;
default:
fputs("Nieznana opcja !\n\r",stderr);
FreeArgv(argv,argc);
return;
}
FreeArgv(argv,argc);
if((Tabfft=(float *)malloc(DimBase*sizeof(float)))==NULL)
return;
if(a<0) a=0;
else if(a>=(int)DimBase) a=(int)DimBase;
if(b<0) b=0;
else if(b>=(int)DimBase) b=(int)DimBase;
if(a>b) { itmp=a; a=b; b=itmp; }
n=b-a;
if(prn==YES)
fprintf(stdout,"<<< FFT >>>\n");
if(ComputeFFT(n,((sig==ORGINAL) ? OrgSygnal+a : (sygnal+DimBase+a)),
Tabfft,window,phase)==-1)
{
free((void *)Tabfft);
return;
}
if(prn==YES)
fprintf(stdout,"<<< ZAPIS DANYCH >>>\n");
if((stream=fopen(filename,"wt"))==NULL)
{
fprintf(stderr,"Nie moge otworzyc pliku %s do pisania !\n",filename);
free((void *)Tabfft);
return;
}
if(SamplingRate!=0.0)
df=SamplingRate/(float)n;
else
df=1.0F;
itmp=n/2;
for(i=0 ; i<=itmp ; i++)
fprintf(stream,"%g %g\n",df*(float)i,Tabfft[itmp-i]);
fclose(stream);
free((void *)Tabfft);
if(prn==YES)
fprintf(stdout,"<<< KONIEC FFT >>>\n");
return;
}
/* Arbitrary Length FFT Adaptacja 1997 01 17
Author:
Jens Joergen Nielsen For non-commercial use only.
Bakkehusene 54 A $100 fee must be paid if used
2970 Hoersholm commercially. Please contact.
DENMARK
e-mail : jnielsen@internet.dk All rights reserved. March 1996.
*/
#define maxPrimeFactor 37
#define maxPrimeFactorDiv2 ((maxPrimeFactor+1)/2)
#define maxFactorCount 20
static double c3_1 = -1.5000000000000E+00; /* c3_1 = cos(2*pi/3)-1; */
static double c3_2 = 8.6602540378444E-01; /* c3_2 = sin(2*pi/3); */
static double c5_1 = -1.2500000000000E+00; /* c5_1 = (cos(u5)+cos(2*u5))/2-1;*/
static double c5_2 = 5.5901699437495E-01; /* c5_2 = (cos(u5)-cos(2*u5))/2; */
static double c5_3 = -9.5105651629515E-01; /* c5_3 = -sin(u5); */
static double c5_4 = -1.5388417685876E+00; /* c5_4 = -(sin(u5)+sin(2*u5)); */
static double c5_5 = 3.6327126400268E-01; /* c5_5 = (sin(u5)-sin(2*u5)); */
static double c8 = 7.0710678118655E-01; /* c8 = 1/sqrt(2); */
static int groupOffset,dataOffset,adr;
static int groupNo,dataNo,blockNo,twNo;
static double omega, tw_re,tw_im;
static double twiddleRe[maxPrimeFactor], twiddleIm[maxPrimeFactor],
trigRe[maxPrimeFactor], trigIm[maxPrimeFactor],
zRe[maxPrimeFactor], zIm[maxPrimeFactor];
static double vRe[maxPrimeFactorDiv2], vIm[maxPrimeFactorDiv2];
static double wRe[maxPrimeFactorDiv2], wIm[maxPrimeFactorDiv2];
static void factorize(int n, int *nFact, int fact[])
{
register int i,j,k;
int nRadix;
int radices[7];
int factors[maxFactorCount];
nRadix = 6;
radices[1]= 2;
radices[2]= 3;
radices[3]= 4;
radices[4]= 5;
radices[5]= 8;
radices[6]= 10;
if (n==1)
{
j=1;
factors[1]=1;
}
else j=0;
i=nRadix;
while ((n>1) && (i>0))
{
if ((n % radices[i]) == 0)
{
n=n / radices[i];
j=j+1;
factors[j]=radices[i];
}
else i=i-1;
}
if (factors[j] == 2) /*substitute factors 2*8 with 4*4 */
{
i = j-1;
while ((i>0) && (factors[i] != 8)) i--;
if (i>0)
{
factors[j] = 4;
factors[i] = 4;
}
}
if (n>1)
{
const int itmp=(int)(sqrt(n)+1.0);
for (k=2; k<itmp; k++)
while ((n % k) == 0)
{
n=n / k;
j=j+1;
factors[j]=k;
}
if (n>1)
{
j=j+1;
factors[j]=n;
}
}
for (i=1; i<=j; i++)
{
fact[i] = factors[j-i+1];
}
*nFact=j;
}
static int transTableSetup(int sofar[], int actual[], int remain[],
int *nFact,
int *nPoints)
{
int i;
factorize(*nPoints,nFact,actual);
if(actual[*nFact]>maxPrimeFactor)
return -1;
remain[0]=*nPoints;
sofar[1]=1;
remain[1]=*nPoints / actual[1];
for (i=2; i<=*nFact; i++)
{
sofar[i]=sofar[i-1]*actual[i-1];
remain[i]=remain[i-1] / actual[i];
}
return 0;
}
static void permute(int nPoint, int nFact,int fact[], int remain[],
double xRe[], double xIm[],double yRe[], double yIm[])
{
register int i,j,k;
int count[maxFactorCount];
for (i=1; i<=nFact; i++) count[i]=0;
k=0;
for (i=0; i<=nPoint-2; i++)
{
yRe[i] = xRe[k];
yIm[i] = xIm[k];
j=1;
k=k+remain[j];
count[1] = count[1]+1;
while (count[j] >= fact[j])
{
count[j]=0;
k=k-remain[j-1]+remain[j+1];
j=j+1;
count[j]=count[j]+1;
}
}
yRe[nPoint-1]=xRe[nPoint-1];
yIm[nPoint-1]=xIm[nPoint-1];
}
static void initTrig(int radix)
{
int i;
double w,xre,xim;
w=2.0*M_PI/radix;
trigRe[0]=1; trigIm[0]=0;
xre=cos(w);
xim=-sin(w);
trigRe[1]=xre; trigIm[1]=xim;
for (i=2; i<radix; i++)
{
trigRe[i]=xre*trigRe[i-1] - xim*trigIm[i-1];
trigIm[i]=xim*trigRe[i-1] + xre*trigIm[i-1];
}
}
static void fft_4(double aRe[], double aIm[])
{
double t1_re,t1_im, t2_re,t2_im;
double m2_re,m2_im, m3_re,m3_im;
t1_re=aRe[0] + aRe[2]; t1_im=aIm[0] + aIm[2];
t2_re=aRe[1] + aRe[3]; t2_im=aIm[1] + aIm[3];
m2_re=aRe[0] - aRe[2]; m2_im=aIm[0] - aIm[2];
m3_re=aIm[1] - aIm[3]; m3_im=aRe[3] - aRe[1];
aRe[0]=t1_re + t2_re; aIm[0]=t1_im + t2_im;
aRe[2]=t1_re - t2_re; aIm[2]=t1_im - t2_im;
aRe[1]=m2_re + m3_re; aIm[1]=m2_im + m3_im;
aRe[3]=m2_re - m3_re; aIm[3]=m2_im - m3_im;
}
static void fft_5(double aRe[], double aIm[])
{
double t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
double t4_re,t4_im, t5_re,t5_im;
double m2_re,m2_im, m3_re,m3_im, m4_re,m4_im;
double m1_re,m1_im, m5_re,m5_im;
double s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
double s4_re,s4_im, s5_re,s5_im;
t1_re=aRe[1] + aRe[4]; t1_im=aIm[1] + aIm[4];
t2_re=aRe[2] + aRe[3]; t2_im=aIm[2] + aIm[3];
t3_re=aRe[1] - aRe[4]; t3_im=aIm[1] - aIm[4];
t4_re=aRe[3] - aRe[2]; t4_im=aIm[3] - aIm[2];
t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
aRe[0]=aRe[0] + t5_re; aIm[0]=aIm[0] + t5_im;
m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
m2_re=c5_2*(t1_re - t2_re); m2_im=c5_2*(t1_im - t2_im);
m3_re=-c5_3*(t3_im + t4_im); m3_im=c5_3*(t3_re + t4_re);
m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;
s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
s1_re=aRe[0] + m1_re; s1_im=aIm[0] + m1_im;
s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;
aRe[1]=s2_re + s3_re; aIm[1]=s2_im + s3_im;
aRe[2]=s4_re + s5_re; aIm[2]=s4_im + s5_im;
aRe[3]=s4_re - s5_re; aIm[3]=s4_im - s5_im;
aRe[4]=s2_re - s3_re; aIm[4]=s2_im - s3_im;
}
static void fft_8(void)
{
double aRe[4], aIm[4], bRe[4], bIm[4], gem;
aRe[0] = zRe[0]; bRe[0] = zRe[1];
aRe[1] = zRe[2]; bRe[1] = zRe[3];
aRe[2] = zRe[4]; bRe[2] = zRe[5];
aRe[3] = zRe[6]; bRe[3] = zRe[7];
aIm[0] = zIm[0]; bIm[0] = zIm[1];
aIm[1] = zIm[2]; bIm[1] = zIm[3];
aIm[2] = zIm[4]; bIm[2] = zIm[5];
aIm[3] = zIm[6]; bIm[3] = zIm[7];
fft_4(aRe, aIm); fft_4(bRe, bIm);
gem = c8*(bRe[1] + bIm[1]);
bIm[1] = c8*(bIm[1] - bRe[1]);
bRe[1] = gem;
gem = bIm[2];
bIm[2] =-bRe[2];
bRe[2] = gem;
gem = c8*(bIm[3] - bRe[3]);
bIm[3] =-c8*(bRe[3] + bIm[3]);
bRe[3] = gem;
zRe[0] = aRe[0] + bRe[0]; zRe[4] = aRe[0] - bRe[0];
zRe[1] = aRe[1] + bRe[1]; zRe[5] = aRe[1] - bRe[1];
zRe[2] = aRe[2] + bRe[2]; zRe[6] = aRe[2] - bRe[2];
zRe[3] = aRe[3] + bRe[3]; zRe[7] = aRe[3] - bRe[3];
zIm[0] = aIm[0] + bIm[0]; zIm[4] = aIm[0] - bIm[0];
zIm[1] = aIm[1] + bIm[1]; zIm[5] = aIm[1] - bIm[1];
zIm[2] = aIm[2] + bIm[2]; zIm[6] = aIm[2] - bIm[2];
zIm[3] = aIm[3] + bIm[3]; zIm[7] = aIm[3] - bIm[3];
}
static void fft_10(void)
{
double aRe[5], aIm[5], bRe[5], bIm[5];
aRe[0] = zRe[0]; bRe[0] = zRe[5];
aRe[1] = zRe[2]; bRe[1] = zRe[7];
aRe[2] = zRe[4]; bRe[2] = zRe[9];
aRe[3] = zRe[6]; bRe[3] = zRe[1];
aRe[4] = zRe[8]; bRe[4] = zRe[3];
aIm[0] = zIm[0]; bIm[0] = zIm[5];
aIm[1] = zIm[2]; bIm[1] = zIm[7];
aIm[2] = zIm[4]; bIm[2] = zIm[9];
aIm[3] = zIm[6]; bIm[3] = zIm[1];
aIm[4] = zIm[8]; bIm[4] = zIm[3];
fft_5(aRe, aIm); fft_5(bRe, bIm);
zRe[0] = aRe[0] + bRe[0]; zRe[5] = aRe[0] - bRe[0];
zRe[6] = aRe[1] + bRe[1]; zRe[1] = aRe[1] - bRe[1];
zRe[2] = aRe[2] + bRe[2]; zRe[7] = aRe[2] - bRe[2];
zRe[8] = aRe[3] + bRe[3]; zRe[3] = aRe[3] - bRe[3];
zRe[4] = aRe[4] + bRe[4]; zRe[9] = aRe[4] - bRe[4];
zIm[0] = aIm[0] + bIm[0]; zIm[5] = aIm[0] - bIm[0];
zIm[6] = aIm[1] + bIm[1]; zIm[1] = aIm[1] - bIm[1];
zIm[2] = aIm[2] + bIm[2]; zIm[7] = aIm[2] - bIm[2];
zIm[8] = aIm[3] + bIm[3]; zIm[3] = aIm[3] - bIm[3];
zIm[4] = aIm[4] + bIm[4]; zIm[9] = aIm[4] - bIm[4];
}
static void fft_odd(int radix)
{
double rere, reim, imre, imim;
register int i,j,k,n,max;
n = radix;
max = (n + 1)/2;
for (j=1; j < max; j++)
{
vRe[j] = zRe[j] + zRe[n-j];
vIm[j] = zIm[j] - zIm[n-j];
wRe[j] = zRe[j] - zRe[n-j];
wIm[j] = zIm[j] + zIm[n-j];
}
for (j=1; j < max; j++)
{
zRe[j]=zRe[0];
zIm[j]=zIm[0];
zRe[n-j]=zRe[0];
zIm[n-j]=zIm[0];
k=j;
for (i=1; i < max; i++)
{
rere = trigRe[k] * vRe[i];
imim = trigIm[k] * vIm[i];
reim = trigRe[k] * wIm[i];
imre = trigIm[k] * wRe[i];
zRe[n-j] += rere + imim;
zIm[n-j] += reim - imre;
zRe[j] += rere - imim;
zIm[j] += reim + imre;
k = k + j;
if (k >= n) k = k - n;
}
}
for (j=1; j < max; j++)
{
zRe[0]=zRe[0] + vRe[j];
zIm[0]=zIm[0] + wIm[j];
}
}
static void twiddleTransf(int sofarRadix, int radix, int remainRadix,
double yRe[], double yIm[])
{ /* twiddleTransf */
double cosw, sinw, gem;
double t1_re,t1_im, t2_re,t2_im, t3_re,t3_im;
double t4_re,t4_im, t5_re,t5_im;
double m2_re,m2_im, m3_re,m3_im, m4_re,m4_im;
double m1_re,m1_im, m5_re,m5_im;
double s1_re,s1_im, s2_re,s2_im, s3_re,s3_im;
double s4_re,s4_im, s5_re,s5_im;
initTrig(radix);
omega = 2.0*M_PI/(double)(sofarRadix*radix);
cosw = cos(omega);
sinw = -sin(omega);
tw_re = 1.0;
tw_im = 0;
dataOffset=0;
groupOffset=dataOffset;
adr=groupOffset;
for (dataNo=0; dataNo<sofarRadix; dataNo++)
{
if (sofarRadix>1)
{
twiddleRe[0] = 1.0;
twiddleIm[0] = 0.0;
twiddleRe[1] = tw_re;
twiddleIm[1] = tw_im;
for (twNo=2; twNo<radix; twNo++)
{
twiddleRe[twNo]=tw_re*twiddleRe[twNo-1]
- tw_im*twiddleIm[twNo-1];
twiddleIm[twNo]=tw_im*twiddleRe[twNo-1]
+ tw_re*twiddleIm[twNo-1];
}
gem = cosw*tw_re - sinw*tw_im;
tw_im = sinw*tw_re + cosw*tw_im;
tw_re = gem;
}
for (groupNo=0; groupNo<remainRadix; groupNo++)
{
if ((sofarRadix>1) && (dataNo > 0))
{
zRe[0]=yRe[adr];
zIm[0]=yIm[adr];
blockNo=1;
do {
adr = adr + sofarRadix;
zRe[blockNo]= twiddleRe[blockNo] * yRe[adr]
- twiddleIm[blockNo] * yIm[adr];
zIm[blockNo]= twiddleRe[blockNo] * yIm[adr]
+ twiddleIm[blockNo] * yRe[adr];
blockNo++;
} while (blockNo < radix);
}
else
for (blockNo=0; blockNo<radix; blockNo++)
{
zRe[blockNo]=yRe[adr];
zIm[blockNo]=yIm[adr];
adr=adr+sofarRadix;
}
switch(radix) {
case 2 : gem=zRe[0] + zRe[1];
zRe[1]=zRe[0] - zRe[1]; zRe[0]=gem;
gem=zIm[0] + zIm[1];
zIm[1]=zIm[0] - zIm[1]; zIm[0]=gem;
break;
case 3 : t1_re=zRe[1] + zRe[2]; t1_im=zIm[1] + zIm[2];
zRe[0]=zRe[0] + t1_re; zIm[0]=zIm[0] + t1_im;
m1_re=c3_1*t1_re; m1_im=c3_1*t1_im;
m2_re=c3_2*(zIm[1] - zIm[2]);
m2_im=c3_2*(zRe[2] - zRe[1]);
s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
zRe[1]=s1_re + m2_re; zIm[1]=s1_im + m2_im;
zRe[2]=s1_re - m2_re; zIm[2]=s1_im - m2_im;
break;
case 4 : t1_re=zRe[0] + zRe[2]; t1_im=zIm[0] + zIm[2];
t2_re=zRe[1] + zRe[3]; t2_im=zIm[1] + zIm[3];
m2_re=zRe[0] - zRe[2]; m2_im=zIm[0] - zIm[2];
m3_re=zIm[1] - zIm[3]; m3_im=zRe[3] - zRe[1];
zRe[0]=t1_re + t2_re; zIm[0]=t1_im + t2_im;
zRe[2]=t1_re - t2_re; zIm[2]=t1_im - t2_im;
zRe[1]=m2_re + m3_re; zIm[1]=m2_im + m3_im;
zRe[3]=m2_re - m3_re; zIm[3]=m2_im - m3_im;
break;
case 5 : t1_re=zRe[1] + zRe[4]; t1_im=zIm[1] + zIm[4];
t2_re=zRe[2] + zRe[3]; t2_im=zIm[2] + zIm[3];
t3_re=zRe[1] - zRe[4]; t3_im=zIm[1] - zIm[4];
t4_re=zRe[3] - zRe[2]; t4_im=zIm[3] - zIm[2];
t5_re=t1_re + t2_re; t5_im=t1_im + t2_im;
zRe[0]=zRe[0] + t5_re; zIm[0]=zIm[0] + t5_im;
m1_re=c5_1*t5_re; m1_im=c5_1*t5_im;
m2_re=c5_2*(t1_re - t2_re);
m2_im=c5_2*(t1_im - t2_im);
m3_re=-c5_3*(t3_im + t4_im);
m3_im=c5_3*(t3_re + t4_re);
m4_re=-c5_4*t4_im; m4_im=c5_4*t4_re;
m5_re=-c5_5*t3_im; m5_im=c5_5*t3_re;
s3_re=m3_re - m4_re; s3_im=m3_im - m4_im;
s5_re=m3_re + m5_re; s5_im=m3_im + m5_im;
s1_re=zRe[0] + m1_re; s1_im=zIm[0] + m1_im;
s2_re=s1_re + m2_re; s2_im=s1_im + m2_im;
s4_re=s1_re - m2_re; s4_im=s1_im - m2_im;
zRe[1]=s2_re + s3_re; zIm[1]=s2_im + s3_im;
zRe[2]=s4_re + s5_re; zIm[2]=s4_im + s5_im;
zRe[3]=s4_re - s5_re; zIm[3]=s4_im - s5_im;
zRe[4]=s2_re - s3_re; zIm[4]=s2_im - s3_im;
break;
case 8 : fft_8(); break;
case 10 : fft_10(); break;
default : fft_odd(radix); break;
}
adr=groupOffset;
for (blockNo=0; blockNo<radix; blockNo++)
{
yRe[adr]=zRe[blockNo]; yIm[adr]=zIm[blockNo];
adr=adr+sofarRadix;
}
groupOffset=groupOffset+sofarRadix*radix;
adr=groupOffset;
}
dataOffset=dataOffset+1;
groupOffset=dataOffset;
adr=groupOffset;
}
}
static int fft(int n, double xRe[], double xIm[],double yRe[], double yIm[])
{
int sofarRadix[maxFactorCount],
actualRadix[maxFactorCount],
remainRadix[maxFactorCount];
int nFactor;
int count;
if(transTableSetup(sofarRadix, actualRadix, remainRadix, &nFactor, &n)==-1)
return -1;
permute(n, nFactor, actualRadix, remainRadix, xRe, xIm, yRe, yIm);
for (count=1; count<=nFactor; count++)
twiddleTransf(sofarRadix[count], actualRadix[count], remainRadix[count],
yRe, yIm);
return 0;
}