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
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
|
/*
This file is part of LPIC++, a particle-in-cell code for
simulating the interaction of laser light with plasma.
Copyright (C) 1994-1997 Roland Lichters
LPIC++ is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
#include <ft2d.h>
//////////////////////////////////////////////////////////////////////////////////////////
FFT2D::FFT2D( int Q_kw, int periods_1, int steps_pp_1, int screen_1,
int periods_2, int steps_pp_2, int screen_2 )
{
if (Q_kw){
periods_input_1 = periods_1;
periods_input_2 = periods_2;
steps_pp_input_1 = steps_pp_1;
steps_pp_input_2 = steps_pp_2;
screen_input_1 = screen_1;
screen_input_2 = screen_2;
steps_input_1 = periods_1 * steps_pp_1;
steps_input_2 = periods_2 * steps_pp_2;
dt_input_1 = (float) periods_input_1 / ( steps_input_1 - 1 );
dt_input_2 = (float) periods_input_2 / ( steps_input_2 - 1 );
steps_1 = steps_ft( steps_input_1 );
steps_2 = steps_ft( steps_input_1 );
steps_half_1 = (int) floor( 0.5*steps_1 + 0.5 );
steps_half_2 = (int) floor( 0.5*steps_2 + 0.5 );
dt_1 = (float) periods_input_1 / ( steps_1 - 1 ); // time step in periods
dt_2 = (float) periods_input_2 / ( steps_2 - 1 ); // time step in periods
df_1 = (float) 1.0 / periods_input_1; // frequency step
df_2 = (float) 1.0 / periods_input_2; // frequency step
nn = new int [ 3 ];
nn[1] = steps_1;
nn[2] = steps_2;
local = fmatrix( 0, steps_1, 0, steps_2 );
data = new float [ 2 * steps_1 * steps_2 + 1 ];
frequency_1 = new float [ steps_1 ];
frequency_2 = new float [ steps_2 ];
// co = fmatrix( 0, steps_half_1+1, 0, steps_2+1 );// pos and neg k, pos frequency!
// si = fmatrix( 0, steps_half_1+1, 0, steps_2+1 );
power = fmatrix( 0, steps_half_1+1, 0, steps_2+1 );
if (!nn || !local || !data || !frequency_1 || !frequency_2 || !power) {
printf( "\n allocation failure in FFT2D::constructor" );
exit(-1);
}
}
}
//////////////////////////////////////////////////////////////////////////////////////////
int FFT2D::steps_ft( int steps_input )
{
int MAX_EXPO = 14;
int expo, steps_ft;
expo = (int) ceil( log(steps_input)/log(2) ); // steps_ft = next power of 2
// larger than steps_input
if (expo > MAX_EXPO) {
expo = MAX_EXPO;
printf( "\n FFT2D: number of steps is 2^%d < %d\n", MAX_EXPO, steps_input );
}
steps_ft = (int) pow( 2, expo );
return steps_ft;
}
//////////////////////////////////////////////////////////////////////////////////////////
float FFT2D::window( float t, int screen_input, int periods_input )
// input: time t in periods
// window cuts off smoothly first and last period
{
float tscr = (float) screen_input;
float toff = (float) periods_input - tscr;
if ( t < tscr ) return pow( sin(0.5*PI*t/tscr), 2 );
else {
if ( t > toff ) return pow( sin(0.5*PI*(1.0-(t-toff)/tscr)), 2 );
else return 1.0;
}
}
//////////////////////////////////////////////////////////////////////////////////////////
void FFT2D::RealFt( float **input )
/*
takes real input matrix [0, ..., steps_input_1 - 1] [0, ..., steps_input_2 - 1 ]
interpolates to local matrix [0, ..., steps_1 - 1] [0, ..., steps_2 - 1],
where steps_1 and steps_2 are powers of 2, usually larger than steps_input
i.e. t_1=0 .... (steps_input_1-1) dt_1
i.e. t_2=0 .... (steps_input_2-1) dt_2
returns real output arrays [0, ... , steps_half_1] [0, ..., steps_2]
i.e. f_1= 0 .... 1/(2*dt_1)
i.e. f_2= -1/(2*dt_2) .... 1/(2*dt_2)
returns cosine-transform co = re
sine-transform si = im
power spectrum pow = 2*(re*re+im*im)
*/
{
int i, index, j;
float t, x;
int th, tl, xh, xl;
float re, im;
for( i=0; i<steps_1; i++ ) // interpolate
{
for( j=0; j<steps_2; j++ )
{
t = (float) i * (steps_input_1-1) / (steps_1-1);
x = (float) j * (steps_input_2-1) / (steps_2-1);
tl = (int) floor( t );
xl = (int) floor( x );
if ( i<steps_1-1) th = tl+1;
else th = tl;
if ( j<steps_2-1) xh = xl+1;
else xh = xl;
t = th - t;
x = xh - x;
local[i][j] = t*x*input[tl][xl] + t*(1.0-x)*input[tl][xh];
local[i][j] += (1.0-t)*x*input[th][xl] + (1.0-t)*(1.0-x)*input[th][xh];
local[i][j] *= window( dt_1*i, screen_input_1, periods_input_1 );
local[i][j] *= window( dt_2*j, screen_input_2, periods_input_2 );
data[2*i*steps_2 + 2*j+1] = local[i][j];
data[2*i*steps_2 + 2*j+2] = 0;
}
}
fftn(data,nn,2,1);
for( i=0; i<=steps_half_1; i++ )
{
if (i==0) index = 0; // only negative frequencies
else index = steps_1 - i; // only negative frequencies
// index = i; // only positive frequencies
frequency_1[i] = df_1 * i;
for( j=0; j<steps_2; j++ ) // positive and negative k-values
{
if (j<steps_half_2) frequency_2[j+steps_half_2] = df_2 * j;
else frequency_2[j-steps_half_2] = df_2 * (j-steps_2);
re = data[2*index*steps_2 + 2*j+1] / (steps_1 * steps_2); // cos-part
im = data[2*index*steps_2 + 2*j+2] / (steps_1 * steps_2); // sin-part
if (j<steps_half_2) {
// co[ i ][ j + steps_half_1 ] = re;
// si[ i ][ j + steps_half_1 ] = im;
power[ i ][ j + steps_half_1 ] = ( re*re+im*im );
}
else {
// co[ i ][ j - steps_half_1 ] = re;
// si[ i ][ j - steps_half_1 ] = im;
power[ i ][ j - steps_half_1 ] = ( re*re+im*im );
}
}
}
}
//////////////////////////////////////////////////////////////////////////////////////////
#define SWAP(a,b) tempr=(a);(a)=(b);(b)=tempr
void FFT2D::fftn(float *data, int *nn, int ndim, int isign)
// numerical recipies routine "fourn.c"
{
int i1,i2,i3,i2rev,i3rev,ip1,ip2,ip3,ifp1,ifp2;
int ibit,idim,k1,k2,n,nprev,nrem,ntot;
float tempi,tempr;
float theta,wi,wpi,wpr,wr,wtemp;
ntot=1;
for (idim=1;idim<=ndim;idim++)
ntot *= nn[idim];
nprev=1;
for (idim=ndim;idim>=1;idim--) {
n=nn[idim];
nrem=ntot/(n*nprev);
ip1=nprev << 1;
ip2=ip1*n;
ip3=ip2*nrem;
i2rev=1;
for (i2=1;i2<=ip2;i2+=ip1) {
if (i2 < i2rev) {
for (i1=i2;i1<=i2+ip1-2;i1+=2) {
for (i3=i1;i3<=ip3;i3+=ip2) {
i3rev=i2rev+i3-i2;
SWAP(data[i3],data[i3rev]);
SWAP(data[i3+1],data[i3rev+1]);
}
}
}
ibit=ip2 >> 1;
while (ibit >= ip1 && i2rev > ibit) {
i2rev -= ibit;
ibit >>= 1;
}
i2rev += ibit;
}
ifp1=ip1;
while (ifp1 < ip2) {
ifp2=ifp1 << 1;
theta=isign*6.28318530717959/(ifp2/ip1);
wtemp=sin(0.5*theta);
wpr = -2.0*wtemp*wtemp;
wpi=sin(theta);
wr=1.0;
wi=0.0;
for (i3=1;i3<=ifp1;i3+=ip1) {
for (i1=i3;i1<=i3+ip1-2;i1+=2) {
for (i2=i1;i2<=ip3;i2+=ifp2) {
k1=i2;
k2=k1+ifp1;
tempr=wr*data[k2]-wi*data[k2+1];
tempi=wr*data[k2+1]+wi*data[k2];
data[k2]=data[k1]-tempr;
data[k2+1]=data[k1+1]-tempi;
data[k1] += tempr;
data[k1+1] += tempi;
}
}
wr=(wtemp=wr)*wpr-wi*wpi+wr;
wi=wi*wpr+wtemp*wpi+wi;
}
ifp1=ifp2;
}
nprev *= n;
}
}
#undef SWAP
//////////////////////////////////////////////////////////////////////////////////////////
//eof
|
