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/* fftr.c
*
* FFT of Real Valued Sequence
*
*
*
* SYNOPSIS:
*
* double x[], sine[];
* int m;
*
* fftr( x, m, sine );
*
*
*
* DESCRIPTION:
*
* Computes the (complex valued) discrete Fourier transform of
* the real valued sequence x[]. The input sequence x[] contains
* n = 2**m samples. The program fills array sine[k] with
* n/4 + 1 values of sin( 2 PI k / n ).
*
* Data format for complex valued output is real part followed
* by imaginary part. The output is developed in the input
* array x[].
*
* The algorithm takes advantage of the fact that the FFT of an
* n point real sequence can be obtained from an n/2 point
* complex FFT.
*
* A radix 2 FFT algorithm is used.
*
* Execution time on an LSI-11/23 with floating point chip
* is 1.0 sec for n = 256.
*
*
*
* REFERENCE:
*
* E. Oran Brigham, The Fast Fourier Transform;
* Prentice-Hall, Inc., 1974
*
*/
#include <math.h>
static short n0 = 0;
static short n4 = 0;
static short msav = 0;
extern double PI;
#ifdef ANSIPROT
extern double sin ( double );
static int bitrv(int, int);
#else
double sin();
static int bitrv();
#endif
fftr( x, m0, sine )
double x[];
int m0;
double sine[];
{
int th, nd, pth, nj, dth, m;
int n, n2, j, k, l, r;
double xr, xi, tr, ti, co, si;
double a, b, c, d, bc, cs, bs, cc;
double *p, *q;
/* Array x assumed filled with real-valued data */
/* m0 = log2(n0) */
/* n0 is the number of real data samples */
if( m0 != msav )
{
msav = m0;
/* Find n0 = 2**m0 */
n0 = 1;
for( j=0; j<m0; j++ )
n0 <<= 1;
n4 = n0 >> 2;
/* Calculate array of sines */
xr = 2.0 * PI / n0;
for( j=0; j<=n4; j++ )
sine[j] = sin( j * xr );
}
n = n0 >> 1; /* doing half length transform */
m = m0 - 1;
/* fftr.c */
/* Complex Fourier Transform of n Complex Data Points */
/* First, bit reverse the input data */
for( k=0; k<n; k++ )
{
j = bitrv( k, m );
if( j > k )
{ /* executed approx. n/2 times */
p = &x[2*k];
tr = *p++;
ti = *p;
q = &x[2*j+1];
*p = *q;
*(--p) = *(--q);
*q++ = tr;
*q = ti;
}
}
/* fftr.c */
/* Radix 2 Complex FFT */
n2 = n/2;
nj = 1;
pth = 1;
dth = 0;
th = 0;
for( l=0; l<m; l++ )
{ /* executed log2(n) times, total */
j = 0;
do
{ /* executed n-1 times, total */
r = th << 1;
si = sine[r];
co = sine[ n4 - r ];
if( j >= pth )
{
th -= dth;
co = -co;
}
else
th += dth;
nd = j;
do
{ /* executed n/2 log2(n) times, total */
r = (nd << 1) + (nj << 1);
p = &x[ r ];
xr = *p++;
xi = *p;
tr = xr * co + xi * si;
ti = xi * co - xr * si;
r = nd << 1;
q = &x[ r ];
xr = *q++;
xi = *q;
*p = xi - ti;
*(--p) = xr - tr;
*q = xi + ti;
*(--q) = xr + tr;
nd += nj << 1;
}
while( nd < n );
}
while( ++j < nj );
n2 >>= 1;
dth = n2;
pth = nj;
nj <<= 1;
}
/* fftr.c */
/* Special trick algorithm */
/* converts to spectrum of real series */
/* Highest frequency term; add space to input array if wanted */
/*
x[2*n] = x[0] - x[1];
x[2*n+1] = 0.0;
*/
/* Zero frequency term */
x[0] = x[0] + x[1];
x[1] = 0.0;
n2 = n/2;
for( j=1; j<=n2; j++ )
{ /* executed n/2 times */
si = sine[j];
co = sine[ n4 - j ];
p = &x[ 2*j ];
xr = *p++;
xi = *p;
q = &x[ 2*(n-j) ];
tr = *q++;
ti = *q;
a = xr + tr;
b = xi + ti;
c = xr - tr;
d = xi - ti;
bc = b * co;
cs = c * si;
bs = b * si;
cc = c * co;
*p = ( d - bs - cc )/2.0;
*(--p) = ( a + bc - cs )/2.0;
*q = -( d + bs + cc )/2.0;
*(--q) = ( a - bc + cs )/2.0;
}
return(0);
}
/* fftr.c */
/* Bit reverser */
int bitrv( j, m )
int j, m;
{
register int j1, ans;
short k;
ans = 0;
j1 = j;
for( k=0; k<m; k++ )
{
ans = (ans << 1) + (j1 & 1);
j1 >>= 1;
}
return( ans );
}
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