1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
|
#include "pv.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. */
static void
bitreverse( float *x, int N );
static float sqr(float x) { return x*x; }
void pv_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;
if ( first ) {
first = 0;
}
theta = PV_PI/N;
wr = 1.;
wi = 0.;
c1 = 0.5;
if ( forward ) {
c2 = -0.5;
pv_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.*sqr( sin( 0.5*theta ));
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
pv_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 pv_cfft( float *x, int NC, int forward )
{
float wr,wi,
wpr,wpi,
theta,
scale;
int mmax,
ND,
m,
i,j,
delta;
ND = NC<<1;
bitreverse( x, ND );
for ( mmax = 2; mmax < ND; mmax = delta ) {
delta = mmax<<1;
theta = PV_2PI/( forward? mmax : -mmax );
wpr = -2.*sqr( sin( 0.5*theta ));
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;
}
}
|
