"Fossies" - the Fresh Open Source Software Archive 
1 /*************************************************************************/
2 /* */
3 /* Centre for Speech Technology Research */
4 /* University of Edinburgh, UK */
5 /* Copyright (c) 1994,1995,1996 */
6 /* All Rights Reserved. */
7 /* */
8 /* Permission is hereby granted, free of charge, to use and distribute */
9 /* this software and its documentation without restriction, including */
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11 /* distribute, sublicense, and/or sell copies of this work, and to */
12 /* permit persons to whom this work is furnished to do so, subject to */
13 /* the following conditions: */
14 /* 1. The code must retain the above copyright notice, this list of */
15 /* conditions and the following disclaimer. */
16 /* 2. Any modifications must be clearly marked as such. */
17 /* 3. Original authors' names are not deleted. */
18 /* 4. The authors' names are not used to endorse or promote products */
19 /* derived from this software without specific prior written */
20 /* permission. */
21 /* */
22 /* THE UNIVERSITY OF EDINBURGH AND THE CONTRIBUTORS TO THIS WORK */
23 /* DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING */
24 /* ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT */
25 /* SHALL THE UNIVERSITY OF EDINBURGH NOR THE CONTRIBUTORS BE LIABLE */
26 /* FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES */
27 /* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN */
28 /* AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, */
29 /* ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF */
30 /* THIS SOFTWARE. */
31 /* */
32 /*************************************************************************/
33 /* Author : Simon King (taken from Tony Robinson) */
34 /* Date : July 1994 */
35 /*-----------------------------------------------------------------------*/
36 /* FFT functions */
37 /* */
38 /*=======================================================================*/
39
40 #include <cmath>
41 //#include <iostream>
42 //#include <fstream>
43 #include "sigpr/EST_fft.h"
44 #include "EST_math.h"
45 #include "EST_error.h"
46
47 #define PI8 0.392699081698724 /* PI / 8.0 */
48 #define RT2 1.4142135623731 /* sqrt(2.0) */
49 #define IRT2 0.707106781186548 /* 1.0/sqrt(2.0) */
50
51 static void FR2TR(int, float*, float*);
52 static void FR4TR(int, int, float*, float*, float*, float*);
53 static void FORD1(int, float*);
54 static void FORD2(int, float*);
55
56 /*
57 ** FAST(b,n)
58 ** This routine replaces the float vector b
59 ** of length n with its finite discrete fourier transform.
60 ** DC term is returned in b[0];
61 ** n/2th harmonic float part in b[1].
62 ** jth harmonic is returned as complex number stored as
63 ** b[2*j] + i b[2*j + 1]
64 ** (i.e., remaining coefficients are as a DPCOMPLEX vector).
65 **
66 */
67
68
69 static int slowFFTsub(EST_FVector &real, EST_FVector &imag, float f)
70 {
71 // f = -1 for FFT, 1 for IFFT
72 // would be nicer if we used a complex number class,
73 // but we don't, so it isn't
74
75 // taken from the FORTRAN old chestnut
76 // in various sig proc books
77 // FORTRAN uses 1..n arrays, so subtract 1 all over the place
78
79
80 float u_real,u_imag;
81 float w_real,w_imag;
82 float t_real,t_imag;
83 float tmp_real,tmp_imag;
84
85 int M,N;
86 int i,j,k,l;
87
88 M = fastlog2(real.n());
89 N = (int)pow(float(2.0),(float)M);
90
91 if (N != real.n())
92 {
93 EST_warning("Illegal FFT order %d", real.n());
94 return -1;
95 }
96
97 for(l=1;l<=M;l++){
98
99 int le = (int)pow(float(2.0),(float)(M+1-l));
100 int le1=le/2;
101
102 u_real = 1.0;
103 u_imag = 0.0;
104
105 w_real=cos(PI/le1);
106 w_imag=f * sin(PI/le1);
107
108 for (j=1;j<=le1;j++)
109 {
110 for (i=j;i<=N-le1;i+=le)
111 {
112 int ip=i+le1;
113 t_real = real.a_no_check(i-1) + real.a_no_check(ip-1);
114 t_imag = imag.a_no_check(i-1) + imag.a_no_check(ip-1);
115
116 tmp_real = real.a_no_check(i-1) - real.a_no_check(ip-1);
117 tmp_imag = imag.a_no_check(i-1) - imag.a_no_check(ip-1);
118
119 real.a_no_check(ip-1) = tmp_real*u_real - tmp_imag*u_imag;
120 imag.a_no_check(ip-1) = tmp_real*u_imag + tmp_imag*u_real;
121
122 real.a_no_check(i-1) = t_real;
123 imag.a_no_check(i-1) = t_imag;
124 }
125
126 tmp_real = u_real*w_real - u_imag*w_imag;
127 tmp_imag = u_real*w_imag + u_imag*w_real;
128
129 u_real=tmp_real;
130 u_imag=tmp_imag;
131
132 }
133
134 }
135
136
137 int NV2=N/2;
138 int NM1=N-1;
139 j=1;
140
141
142 for (i=1; i<=NM1;i++)
143 {
144 if (i < j)
145 {
146 t_real=real(j-1);
147 t_imag=imag(j-1);
148
149 real[j-1] = real(i-1);
150 imag[j-1] = imag(i-1);
151
152 real[i-1] = t_real;
153 imag[i-1] = t_imag;
154
155 }
156
157 k=NV2;
158
159 while(k < j)
160 {
161 j=j-k;
162 k=k/2;
163 }
164
165 j=j+k;
166
167 }
168
169 return 0;
170 }
171
172
173 int slowFFT(EST_FVector &real, EST_FVector &imag)
174 {
175 return slowFFTsub(real,imag,-1.0);
176 }
177
178
179 int slowIFFT(EST_FVector &real, EST_FVector &imag)
180 {
181 int N=real.n();
182 if (N <=0 )
183 return -1;
184
185 if (slowFFTsub(real,imag,1.0) != 0)
186 return -1;
187
188 for(int i=1;i<=N;i++){
189 real[i-1] /= (float)N;
190 imag[i-1] /= (float)N;
191 }
192
193 return 0;
194 }
195
196
197 int energy_spectrum(EST_FVector &real, EST_FVector &imag)
198 {
199 if (slowFFT(real, imag) != 0)
200 return -1;
201
202 int i;
203 for(i=0;i<real.n();i++)
204 real[i] = imag[i] = (real(i)*real(i) + imag(i)*imag(i));
205
206 return 0;
207 }
208
209 int power_spectrum_slow(EST_FVector &real, EST_FVector &imag)
210 {
211
212 if (slowFFT(real,imag) != 0)
213 return -1;
214
215 int i;
216 for(i=0;i<real.n();i++)
217 real[i] = imag[i] = sqrt((real(i)*real(i) + imag(i)*imag(i)));
218
219 return 0;
220 }
221
222 int power_spectrum(EST_FVector &real, EST_FVector &imag)
223 {
224
225 if (fastFFT(real) == 0)
226 return -1;
227
228 int i,j,k;
229 int n=real.n();
230 for(i=0,j=0, k=1;i<n;i+=2,j++,k+=2)
231 real.a_no_check(j)
232 = imag.a_no_check(j)
233 = sqrt((real.a_no_check(i)*real.a_no_check(i)
234 + real.a_no_check(k)*real.a_no_check(k)));
235
236 return 0;
237 }
238
239 // the following code is not by Simon King, as you can see
240 /*
241 ** Discrete Fourier analysis routine
242 ** from IEEE Programs for Digital Signal Processing
243 ** G. D. Bergland and M. T. Dolan, original authors
244 ** Translated from the FORTRAN with some changes by Paul Kube
245 **
246 ** Modified to return the power spectrum by Chuck Wooters
247 **
248 ** Modified again by Tony Robinson (ajr@eng.cam.ac.uk) Dec 92
249 **
250 ** Modified to use EST_FVector class Simon King (simonk@cstr.ed.ac.uk) Nov 96
251 **
252 */
253
254 #define signum(i) (i < 0 ? -1 : i == 0 ? 0 : 1)
255
256 int fastFFT(EST_FVector &invec)
257 {
258 // Tony Robinsons
259 int i, in, nn, n2pow, n4pow;
260
261 // we could modify all the code to use vector classes ....
262 // ... or we could do this:
263
264 // TO DO
265 // use FSimpleVector::copy_section here
266
267 // quick fix
268 int n=invec.n(); // order
269
270 #if 0
271 float *b = new float[n];
272 for(i=0; i<n; i++)
273 b[i] = invec(i);
274 #endif
275 float *b=invec.memory();
276
277 n2pow = fastlog2(n);
278 if (n2pow <= 0) return 0;
279 n4pow = n2pow / 2;
280
281 /* radix 2 iteration required; do it now */
282 if (n2pow % 2)
283 {
284 nn = 2;
285 in = n / nn;
286 FR2TR(in, b, b + in );
287 }
288 else nn = 1;
289
290 /* perform radix 4 iterations */
291 for(i = 1; i <= n4pow; i++) {
292 nn *= 4;
293 in = n / nn;
294 FR4TR(in, nn, b, b + in, b + 2 * in, b + 3 * in);
295 }
296
297 /* perform inplace reordering */
298 FORD1(n2pow, b);
299 FORD2(n2pow, b);
300
301 /* take conjugates */
302 for(i = 3; i < n; i += 2) b[i] = -b[i];
303
304 #if 0
305 // copy back
306 for(i=0; i<n; i++)
307 invec[i] = b[i];
308 #endif
309
310 return 1;
311 }
312
313 /* radix 2 subroutine */
314 void FR2TR(int in, float *b0, float *b1)
315 {
316 int k;
317 float t;
318 for (k = 0; k < in; k++)
319 {
320 t = b0[k] + b1[k];
321 b1[k] = b0[k] - b1[k];
322 b0[k] = t;
323 }
324 }
325
326 /* radix 4 subroutine */
327 void FR4TR(int in, int nn, float *b0, float *b1, float *b2, float* b3) {
328 float arg, piovn, th2;
329 float *b4 = b0, *b5 = b1, *b6 = b2, *b7 = b3;
330 float t0, t1, t2, t3, t4, t5, t6, t7;
331 float r1, r5, pr, pi;
332 float c1, c2, c3, s1, s2, s3;
333
334 int j, k, jj, kk, jthet, jlast, ji, jl, jr, int4;
335 int L[16], L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15;
336 int j0, j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12, j13, j14;
337 int k0, kl;
338
339 L[1] = nn / 4;
340 for(k = 2; k < 16; k++) { /* set up L's */
341 switch (signum(L[k-1] - 2)) {
342 case -1:
343 L[k-1]=2;
344 case 0:
345 L[k]=2;
346 break;
347 case 1:
348 L[k]=L[k-1]/2;
349 }
350 }
351
352 L15=L[1]; L14=L[2]; L13=L[3]; L12=L[4]; L11=L[5]; L10=L[6]; L9=L[7];
353 L8=L[8]; L7=L[9]; L6=L[10]; L5=L[11]; L4=L[12]; L3=L[13]; L2=L[14];
354 L1=L[15];
355
356 piovn = PI / nn;
357 ji=3;
358 jl=2;
359 jr=2;
360
361 for(j1=2;j1<=L1;j1+=2)
362 for(j2=j1;j2<=L2;j2+=L1)
363 for(j3=j2;j3<=L3;j3+=L2)
364 for(j4=j3;j4<=L4;j4+=L3)
365 for(j5=j4;j5<=L5;j5+=L4)
366 for(j6=j5;j6<=L6;j6+=L5)
367 for(j7=j6;j7<=L7;j7+=L6)
368 for(j8=j7;j8<=L8;j8+=L7)
369 for(j9=j8;j9<=L9;j9+=L8)
370 for(j10=j9;j10<=L10;j10+=L9)
371 for(j11=j10;j11<=L11;j11+=L10)
372 for(j12=j11;j12<=L12;j12+=L11)
373 for(j13=j12;j13<=L13;j13+=L12)
374 for(j14=j13;j14<=L14;j14+=L13)
375 for(jthet=j14;jthet<=L15;jthet+=L14)
376 {
377 th2 = jthet - 2;
378 if(th2<=0.0)
379 {
380 for(k=0;k<in;k++)
381 {
382 t0 = b0[k] + b2[k];
383 t1 = b1[k] + b3[k];
384 b2[k] = b0[k] - b2[k];
385 b3[k] = b1[k] - b3[k];
386 b0[k] = t0 + t1;
387 b1[k] = t0 - t1;
388 }
389 if(nn-4>0)
390 {
391 k0 = in*4 + 1;
392 kl = k0 + in - 1;
393 for (k=k0;k<=kl;k++)
394 {
395 kk = k-1;
396 pr = IRT2 * (b1[kk]-b3[kk]);
397 pi = IRT2 * (b1[kk]+b3[kk]);
398 b3[kk] = b2[kk] + pi;
399 b1[kk] = pi - b2[kk];
400 b2[kk] = b0[kk] - pr;
401 b0[kk] = b0[kk] + pr;
402 }
403 }
404 }
405 else
406 {
407 arg = th2*piovn;
408 c1 = cos(arg);
409 s1 = sin(arg);
410 c2 = c1*c1 - s1*s1;
411 s2 = c1*s1 + c1*s1;
412 c3 = c1*c2 - s1*s2;
413 s3 = c2*s1 + s2*c1;
414
415 int4 = in*4;
416 j0=jr*int4 + 1;
417 k0=ji*int4 + 1;
418 jlast = j0+in-1;
419 for(j=j0;j<=jlast;j++)
420 {
421 k = k0 + j - j0;
422 kk = k-1; jj = j-1;
423 r1 = b1[jj]*c1 - b5[kk]*s1;
424 r5 = b1[jj]*s1 + b5[kk]*c1;
425 t2 = b2[jj]*c2 - b6[kk]*s2;
426 t6 = b2[jj]*s2 + b6[kk]*c2;
427 t3 = b3[jj]*c3 - b7[kk]*s3;
428 t7 = b3[jj]*s3 + b7[kk]*c3;
429 t0 = b0[jj] + t2;
430 t4 = b4[kk] + t6;
431 t2 = b0[jj] - t2;
432 t6 = b4[kk] - t6;
433 t1 = r1 + t3;
434 t5 = r5 + t7;
435 t3 = r1 - t3;
436 t7 = r5 - t7;
437 b0[jj] = t0 + t1;
438 b7[kk] = t4 + t5;
439 b6[kk] = t0 - t1;
440 b1[jj] = t5 - t4;
441 b2[jj] = t2 - t7;
442 b5[kk] = t6 + t3;
443 b4[kk] = t2 + t7;
444 b3[jj] = t3 - t6;
445 }
446 jr += 2;
447 ji -= 2;
448 if(ji-jl <= 0) {
449 ji = 2*jr - 1;
450 jl = jr;
451 }
452 }
453 }
454 }
455
456 /* an inplace reordering subroutine */
457 void FORD1(int m, float *b) {
458 int j, k = 4, kl = 2, n = 0x1 << m;
459 float t;
460
461 for(j = 4; j <= n; j += 2) {
462 if (k - j>0) {
463 t = b[j-1];
464 b[j - 1] = b[k - 1];
465 b[k - 1] = t;
466 }
467 k -= 2;
468 if (k - kl <= 0) {
469 k = 2*j;
470 kl = j;
471 }
472 }
473 }
474
475 /* the other inplace reordering subroutine */
476 void FORD2(int m, float *b)
477 {
478 float t;
479
480 int n = 0x1<<m, k, ij, ji, ij1, ji1;
481
482 int l[16], l1, l2, l3, l4, l5, l6, l7, l8, l9, l10, l11, l12, l13, l14, l15;
483 int j1, j2, j3, j4, j5, j6, j7, j8, j9, j10, j11, j12, j13, j14;
484
485
486 l[1] = n;
487 for(k=2;k<=m;k++) l[k]=l[k-1]/2;
488 for(k=m;k<=14;k++) l[k+1]=2;
489
490 l15=l[1];l14=l[2];l13=l[3];l12=l[4];l11=l[5];l10=l[6];l9=l[7];
491 l8=l[8];l7=l[9];l6=l[10];l5=l[11];l4=l[12];l3=l[13];l2=l[14];l1=l[15];
492
493 ij = 2;
494
495 for(j1=2;j1<=l1;j1+=2)
496 for(j2=j1;j2<=l2;j2+=l1)
497 for(j3=j2;j3<=l3;j3+=l2)
498 for(j4=j3;j4<=l4;j4+=l3)
499 for(j5=j4;j5<=l5;j5+=l4)
500 for(j6=j5;j6<=l6;j6+=l5)
501 for(j7=j6;j7<=l7;j7+=l6)
502 for(j8=j7;j8<=l8;j8+=l7)
503 for(j9=j8;j9<=l9;j9+=l8)
504 for(j10=j9;j10<=l10;j10+=l9)
505 for(j11=j10;j11<=l11;j11+=l10)
506 for(j12=j11;j12<=l12;j12+=l11)
507 for(j13=j12;j13<=l13;j13+=l12)
508 for(j14=j13;j14<=l14;j14+=l13)
509 for(ji=j14;ji<=l15;ji+=l14) {
510 ij1 = ij-1; ji1 = ji - 1;
511 if(ij-ji<0) {
512 t = b[ij1-1];
513 b[ij1-1]=b[ji1-1];
514 b[ji1-1] = t;
515
516 t = b[ij1];
517 b[ij1]=b[ji1];
518 b[ji1] = t;
519 }
520 ij += 2;
521 }
522 }
523
524 int fastlog2(int n) {
525 int num_bits, power = 0;
526
527 if ((n < 2) || (n % 2 != 0)) return(0);
528 num_bits = sizeof(int) * 8; /* How big are ints on this machine? */
529
530 while(power <= num_bits) {
531 n >>= 1;
532 power += 1;
533 if (n & 0x01) {
534 if (n > 1) return(0);
535 else return(power);
536 }
537 }
538 return(0);
539 }
2.4-release_vs_2.5.0-release.