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#include "fftease.h"
/* If forward is true, rfft replaces 2*N real data points in x with
N complex values representing the positive frequency half of their
Fourier spectrum, with x[1] replaced with the real part of the Nyquist
frequency value. If forward is false, rfft expects x to contain a
positive frequency spectrum arranged as before, and replaces it with
2*N real values. N MUST be a power of 2. */
void rfft( float *x, int N, int forward )
{
float c1,c2,
h1r,h1i,
h2r,h2i,
wr,wi,
wpr,wpi,
temp,
theta;
float xr,xi;
int i,
i1,i2,i3,i4,
N2p1;
static int first = 1;
/*float PI, TWOPI;*/
void cfft();
if ( first ) {
first = 0;
}
theta = PI/N;
wr = 1.;
wi = 0.;
c1 = 0.5;
if ( forward ) {
c2 = -0.5;
cfft( x, N, forward );
xr = x[0];
xi = x[1];
} else {
c2 = 0.5;
theta = -theta;
xr = x[1];
xi = 0.;
x[1] = 0.;
}
wpr = -2.*pow( sin( 0.5*theta ), 2. );
wpi = sin( theta );
N2p1 = (N<<1) + 1;
for ( i = 0; i <= N>>1; i++ ) {
i1 = i<<1;
i2 = i1 + 1;
i3 = N2p1 - i2;
i4 = i3 + 1;
if ( i == 0 ) {
h1r = c1*(x[i1] + xr );
h1i = c1*(x[i2] - xi );
h2r = -c2*(x[i2] + xi );
h2i = c2*(x[i1] - xr );
x[i1] = h1r + wr*h2r - wi*h2i;
x[i2] = h1i + wr*h2i + wi*h2r;
xr = h1r - wr*h2r + wi*h2i;
xi = -h1i + wr*h2i + wi*h2r;
} else {
h1r = c1*(x[i1] + x[i3] );
h1i = c1*(x[i2] - x[i4] );
h2r = -c2*(x[i2] + x[i4] );
h2i = c2*(x[i1] - x[i3] );
x[i1] = h1r + wr*h2r - wi*h2i;
x[i2] = h1i + wr*h2i + wi*h2r;
x[i3] = h1r - wr*h2r + wi*h2i;
x[i4] = -h1i + wr*h2i + wi*h2r;
}
wr = (temp = wr)*wpr - wi*wpi + wr;
wi = wi*wpr + temp*wpi + wi;
}
if ( forward )
x[1] = xr;
else
cfft( x, N, forward );
}
/* cfft replaces float array x containing NC complex values
(2*NC float values alternating real, imagininary, etc.)
by its Fourier transform if forward is true, or by its
inverse Fourier transform if forward is false, using a
recursive Fast Fourier transform method due to Danielson
and Lanczos. NC MUST be a power of 2. */
void cfft( float *x, int NC, int forward )
{
float wr,wi,
wpr,wpi,
theta,
scale;
int mmax,
ND,
m,
i,j,
delta;
void bitreverse();
ND = NC<<1;
bitreverse( x, ND );
for ( mmax = 2; mmax < ND; mmax = delta ) {
delta = mmax<<1;
theta = TWOPI/( forward? mmax : -mmax );
wpr = -2.*pow( sin( 0.5*theta ), 2. );
wpi = sin( theta );
wr = 1.;
wi = 0.;
for ( m = 0; m < mmax; m += 2 ) {
register float rtemp, itemp;
for ( i = m; i < ND; i += delta ) {
j = i + mmax;
rtemp = wr*x[j] - wi*x[j+1];
itemp = wr*x[j+1] + wi*x[j];
x[j] = x[i] - rtemp;
x[j+1] = x[i+1] - itemp;
x[i] += rtemp;
x[i+1] += itemp;
}
wr = (rtemp = wr)*wpr - wi*wpi + wr;
wi = wi*wpr + rtemp*wpi + wi;
}
}
/* scale output */
scale = forward ? 1./ND : 2.;
{ register float *xi=x, *xe=x+ND;
while ( xi < xe )
*xi++ *= scale;
}
}
/* bitreverse places float array x containing N/2 complex values
into bit-reversed order */
void bitreverse( float *x, int N )
{
float rtemp,itemp;
int i,j,
m;
for ( i = j = 0; i < N; i += 2, j += m ) {
if ( j > i ) {
rtemp = x[j]; itemp = x[j+1]; /* complex exchange */
x[j] = x[i]; x[j+1] = x[i+1];
x[i] = rtemp; x[i+1] = itemp;
}
for ( m = N>>1; m >= 2 && j >= m; m >>= 1 )
j -= m;
}
}
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