source: src/spectral/fft.c @ 3f90b7a

feature/autosinkfeature/cnnfeature/cnn_orgfeature/constantqfeature/crepefeature/crepe_orgfeature/pitchshiftfeature/pydocstringsfeature/timestretchfix/ffmpeg5
Last change on this file since 3f90b7a was 3f90b7a, checked in by Paul Brossier <piem@piem.org>, 7 years ago

src/spectral/fft.c: remove unrequired scaling, fixing python unit tests
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1/*
2  Copyright (C) 2003-2009 Paul Brossier <piem@aubio.org>
3
4  This file is part of aubio.
5
6  aubio is free software: you can redistribute it and/or modify
7  it under the terms of the GNU General Public License as published by
8  the Free Software Foundation, either version 3 of the License, or
9  (at your option) any later version.
10
11  aubio is distributed in the hope that it will be useful,
12  but WITHOUT ANY WARRANTY; without even the implied warranty of
13  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14  GNU General Public License for more details.
15
16  You should have received a copy of the GNU General Public License
17  along with aubio.  If not, see <http://www.gnu.org/licenses/>.
18
19*/
20
21#include "aubio_priv.h"
22#include "fvec.h"
23#include "cvec.h"
24#include "mathutils.h"
25#include "spectral/fft.h"
26
27#ifdef HAVE_FFTW3             // using FFTW3
28/* note that <complex.h> is not included here but only in aubio_priv.h, so that
29 * c++ projects can still use their own complex definition. */
30#include <fftw3.h>
31#include <pthread.h>
32
33#ifdef HAVE_COMPLEX_H
34#ifdef HAVE_FFTW3F
35/** fft data type with complex.h and fftw3f */
36#define FFTW_TYPE fftwf_complex
37#else
38/** fft data type with complex.h and fftw3 */
39#define FFTW_TYPE fftw_complex
40#endif
41#else
42#ifdef HAVE_FFTW3F
43/** fft data type without complex.h and with fftw3f */
44#define FFTW_TYPE float
45#else
46/** fft data type without complex.h and with fftw */
47#define FFTW_TYPE double
48#endif
49#endif
50
51/** fft data type */
52typedef FFTW_TYPE fft_data_t;
53
54#ifdef HAVE_FFTW3F
55#define fftw_malloc            fftwf_malloc
56#define fftw_free              fftwf_free
57#define fftw_execute           fftwf_execute
58#define fftw_plan_dft_r2c_1d   fftwf_plan_dft_r2c_1d
59#define fftw_plan_dft_c2r_1d   fftwf_plan_dft_c2r_1d
60#define fftw_plan_r2r_1d       fftwf_plan_r2r_1d
61#define fftw_plan              fftwf_plan
62#define fftw_destroy_plan      fftwf_destroy_plan
63#endif
64
65#ifdef HAVE_FFTW3F
66#if HAVE_AUBIO_DOUBLE
67#error "Using aubio in double precision with fftw3 in single precision"
68#endif /* HAVE_AUBIO_DOUBLE */
69#define real_t float
70#elif defined (HAVE_FFTW3) /* HAVE_FFTW3F */
71#if !HAVE_AUBIO_DOUBLE
72#error "Using aubio in single precision with fftw3 in double precision"
73#endif /* HAVE_AUBIO_DOUBLE */
74#define real_t double
75#endif /* HAVE_FFTW3F */
76
77// a global mutex for FFTW thread safety
78pthread_mutex_t aubio_fftw_mutex = PTHREAD_MUTEX_INITIALIZER;
79
80#elif defined HAVE_ACCELERATE        // using ACCELERATE
81// https://developer.apple.com/library/mac/#documentation/Accelerate/Reference/vDSPRef/Reference/reference.html
82#include <Accelerate/Accelerate.h>
83
84#if !HAVE_AUBIO_DOUBLE
85#define aubio_vDSP_ctoz                vDSP_ctoz
86#define aubio_vDSP_fft_zrip            vDSP_fft_zrip
87#define aubio_vDSP_ztoc                vDSP_ztoc
88#define aubio_vDSP_zvmags              vDSP_zvmags
89#define aubio_vDSP_zvphas              vDSP_zvphas
90#define aubio_vDSP_vsadd               vDSP_vsadd
91#define aubio_vDSP_vsmul               vDSP_vsmul
92#define aubio_vDSP_create_fftsetup     vDSP_create_fftsetup
93#define aubio_vDSP_destroy_fftsetup    vDSP_destroy_fftsetup
94#define aubio_DSPComplex               DSPComplex
95#define aubio_DSPSplitComplex          DSPSplitComplex
96#define aubio_FFTSetup                 FFTSetup
97#define aubio_vvsqrt                   vvsqrtf
98#else
99#define aubio_vDSP_ctoz                vDSP_ctozD
100#define aubio_vDSP_fft_zrip            vDSP_fft_zripD
101#define aubio_vDSP_ztoc                vDSP_ztocD
102#define aubio_vDSP_zvmags              vDSP_zvmagsD
103#define aubio_vDSP_zvphas              vDSP_zvphasD
104#define aubio_vDSP_vsadd               vDSP_vsaddD
105#define aubio_vDSP_vsmul               vDSP_vsmulD
106#define aubio_vDSP_create_fftsetup     vDSP_create_fftsetupD
107#define aubio_vDSP_destroy_fftsetup    vDSP_destroy_fftsetupD
108#define aubio_DSPComplex               DSPDoubleComplex
109#define aubio_DSPSplitComplex          DSPDoubleSplitComplex
110#define aubio_FFTSetup                 FFTSetupD
111#define aubio_vvsqrt                   vvsqrt
112#endif /* HAVE_AUBIO_DOUBLE */
113
114#elif defined HAVE_INTEL_IPP // using INTEL IPP
115
116#if !HAVE_AUBIO_DOUBLE
117#define aubio_IppFloat                 Ipp32f
118#define aubio_IppComplex               Ipp32fc
119#define aubio_FFTSpec                  FFTSpec_R_32f
120#define aubio_ippsPhas                 ippsPhase_32fc
121#define aubio_ippsMalloc_complex       ippsMalloc_32fc
122#define aubio_ippsFFTInit_R            ippsFFTInit_R_32f
123#define aubio_ippsFFTGetSize_R         ippsFFTGetSize_R_32f
124#define aubio_ippsFFTInv_CCSToR        ippsFFTInv_CCSToR_32f
125#define aubio_ippsFFTFwd_RToCCS        ippsFFTFwd_RToCCS_32f
126#else /* HAVE_AUBIO_DOUBLE */
127#define aubio_IppFloat                 Ipp64f
128#define aubio_IppComplex               Ipp64fc
129#define aubio_FFTSpec                  FFTSpec_R_64f
130#define aubio_ippsPhas                 ippsPhase_64fc
131#define aubio_ippsMalloc_complex       ippsMalloc_64fc
132#define aubio_ippsFFTInit_R            ippsFFTInit_R_64f
133#define aubio_ippsFFTGetSize_R         ippsFFTGetSize_R_64f
134#define aubio_ippsFFTInv_CCSToR        ippsFFTInv_CCSToR_64f
135#define aubio_ippsFFTFwd_RToCCS        ippsFFTFwd_RToCCS_64f
136#endif
137
138
139#else // using OOURA
140// let's use ooura instead
141extern void aubio_ooura_rdft(int, int, smpl_t *, int *, smpl_t *);
142
143#endif
144
145struct _aubio_fft_t {
146  uint_t winsize;
147  uint_t fft_size;
148
149#ifdef HAVE_FFTW3             // using FFTW3
150  real_t *in, *out;
151  fftw_plan pfw, pbw;
152  fft_data_t * specdata; /* complex spectral data */
153
154#elif defined HAVE_ACCELERATE  // using ACCELERATE
155  int log2fftsize;
156  aubio_FFTSetup fftSetup;
157  aubio_DSPSplitComplex spec;
158  smpl_t *in, *out;
159 
160#elif defined HAVE_INTEL_IPP  // using Intel IPP
161  // mark FFT impl as Intel IPP
162  #define INTEL_IPP_FFT 1
163  smpl_t *in, *out;
164  Ipp8u* memSpec;
165  Ipp8u* memInit;
166  Ipp8u* memBuffer;
167  struct aubio_FFTSpec* fftSpec;
168  aubio_IppComplex* complexOut;
169#else                         // using OOURA
170  smpl_t *in, *out;
171  smpl_t *w;
172  int *ip;
173#endif /* using OOURA */
174
175  fvec_t * compspec;
176};
177
178aubio_fft_t * new_aubio_fft (uint_t winsize) {
179  aubio_fft_t * s = AUBIO_NEW(aubio_fft_t);
180  if ((sint_t)winsize < 2) {
181    AUBIO_ERR("fft: got winsize %d, but can not be < 2\n", winsize);
182    goto beach;
183  }
184
185#ifdef HAVE_FFTW3
186  uint_t i;
187  s->winsize  = winsize;
188  /* allocate memory */
189  s->in       = AUBIO_ARRAY(real_t,winsize);
190  s->out      = AUBIO_ARRAY(real_t,winsize);
191  s->compspec = new_fvec(winsize);
192  /* create plans */
193  pthread_mutex_lock(&aubio_fftw_mutex);
194#ifdef HAVE_COMPLEX_H
195  s->fft_size = winsize/2 + 1;
196  s->specdata = (fft_data_t*)fftw_malloc(sizeof(fft_data_t)*s->fft_size);
197  s->pfw = fftw_plan_dft_r2c_1d(winsize, s->in,  s->specdata, FFTW_ESTIMATE);
198  s->pbw = fftw_plan_dft_c2r_1d(winsize, s->specdata, s->out, FFTW_ESTIMATE);
199#else
200  s->fft_size = winsize;
201  s->specdata = (fft_data_t*)fftw_malloc(sizeof(fft_data_t)*s->fft_size);
202  s->pfw = fftw_plan_r2r_1d(winsize, s->in,  s->specdata, FFTW_R2HC, FFTW_ESTIMATE);
203  s->pbw = fftw_plan_r2r_1d(winsize, s->specdata, s->out, FFTW_HC2R, FFTW_ESTIMATE);
204#endif
205  pthread_mutex_unlock(&aubio_fftw_mutex);
206  for (i = 0; i < s->winsize; i++) {
207    s->in[i] = 0.;
208    s->out[i] = 0.;
209  }
210  for (i = 0; i < s->fft_size; i++) {
211    s->specdata[i] = 0.;
212  }
213
214#elif defined HAVE_ACCELERATE  // using ACCELERATE
215  s->winsize = winsize;
216  s->fft_size = winsize;
217  s->compspec = new_fvec(winsize);
218  s->log2fftsize = aubio_power_of_two_order(s->fft_size);
219  s->in = AUBIO_ARRAY(smpl_t, s->fft_size);
220  s->out = AUBIO_ARRAY(smpl_t, s->fft_size);
221  s->spec.realp = AUBIO_ARRAY(smpl_t, s->fft_size/2);
222  s->spec.imagp = AUBIO_ARRAY(smpl_t, s->fft_size/2);
223  s->fftSetup = aubio_vDSP_create_fftsetup(s->log2fftsize, FFT_RADIX2);
224
225#elif defined HAVE_INTEL_IPP  // using Intel IPP
226  const IppHintAlgorithm qualityHint = ippAlgHintAccurate; // OR ippAlgHintFast;
227  const int flags = IPP_FFT_NODIV_BY_ANY; // we're scaling manually afterwards
228  int order = aubio_power_of_two_order(winsize);
229  int sizeSpec, sizeInit, sizeBuffer;
230  IppStatus status;
231
232  if (winsize <= 4 || aubio_is_power_of_two(winsize) != 1)
233  {
234    AUBIO_ERR("intel IPP fft: can only create with sizes > 4 and power of two, requested %d,"
235      " try recompiling aubio with --enable-fftw3\n", winsize);
236    goto beach;
237  }
238
239  status = aubio_ippsFFTGetSize_R(order, flags, qualityHint,
240      &sizeSpec, &sizeInit, &sizeBuffer);
241  if (status != ippStsNoErr) {
242    AUBIO_ERR("fft: failed to initialize fft. IPP error: %d\n", status);
243    goto beach;
244  }
245  s->fft_size = s->winsize = winsize;
246  s->compspec = new_fvec(winsize);
247  s->in = AUBIO_ARRAY(smpl_t, s->winsize);
248  s->out = AUBIO_ARRAY(smpl_t, s->winsize);
249  s->memSpec = ippsMalloc_8u(sizeSpec);
250  s->memBuffer = ippsMalloc_8u(sizeBuffer);
251  if (sizeInit > 0 ) {
252    s->memInit = ippsMalloc_8u(sizeInit);
253  }
254  s->complexOut = aubio_ippsMalloc_complex(s->fft_size / 2 + 1);
255  status = aubio_ippsFFTInit_R(
256    &s->fftSpec, order, flags, qualityHint, s->memSpec, s->memInit);
257  if (status != ippStsNoErr) {
258    AUBIO_ERR("fft: failed to initialize. IPP error: %d\n", status);
259    goto beach;
260  }
261
262#else                         // using OOURA
263  if (aubio_is_power_of_two(winsize) != 1) {
264    AUBIO_ERR("fft: can only create with sizes power of two, requested %d,"
265        " try recompiling aubio with --enable-fftw3\n", winsize);
266    goto beach;
267  }
268  s->winsize = winsize;
269  s->fft_size = winsize / 2 + 1;
270  s->compspec = new_fvec(winsize);
271  s->in    = AUBIO_ARRAY(smpl_t, s->winsize);
272  s->out   = AUBIO_ARRAY(smpl_t, s->winsize);
273  s->ip    = AUBIO_ARRAY(int   , s->fft_size);
274  s->w     = AUBIO_ARRAY(smpl_t, s->fft_size);
275  s->ip[0] = 0;
276#endif /* using OOURA */
277
278  return s;
279
280beach:
281  AUBIO_FREE(s);
282  return NULL;
283}
284
285void del_aubio_fft(aubio_fft_t * s) {
286  /* destroy data */
287#ifdef HAVE_FFTW3             // using FFTW3
288  pthread_mutex_lock(&aubio_fftw_mutex);
289  fftw_destroy_plan(s->pfw);
290  fftw_destroy_plan(s->pbw);
291  fftw_free(s->specdata);
292  pthread_mutex_unlock(&aubio_fftw_mutex);
293
294#elif defined HAVE_ACCELERATE // using ACCELERATE
295  AUBIO_FREE(s->spec.realp);
296  AUBIO_FREE(s->spec.imagp);
297  aubio_vDSP_destroy_fftsetup(s->fftSetup);
298
299#elif defined HAVE_INTEL_IPP  // using Intel IPP
300  ippFree(s->memSpec);
301  ippFree(s->memInit);
302  ippFree(s->memBuffer);
303  ippFree(s->complexOut);
304
305#else                         // using OOURA
306  AUBIO_FREE(s->w);
307  AUBIO_FREE(s->ip);
308#endif
309
310  del_fvec(s->compspec);
311  AUBIO_FREE(s->in);
312  AUBIO_FREE(s->out);
313  AUBIO_FREE(s);
314}
315
316void aubio_fft_do(aubio_fft_t * s, const fvec_t * input, cvec_t * spectrum) {
317  aubio_fft_do_complex(s, input, s->compspec);
318  aubio_fft_get_spectrum(s, s->compspec, spectrum);
319}
320
321void aubio_fft_rdo(aubio_fft_t * s, const cvec_t * spectrum, fvec_t * output) {
322  aubio_fft_get_realimag(s, spectrum, s->compspec);
323  aubio_fft_rdo_complex(s, s->compspec, output);
324}
325
326void aubio_fft_do_complex(aubio_fft_t * s, const fvec_t * input, fvec_t * compspec) {
327  uint_t i;
328#ifndef HAVE_MEMCPY_HACKS
329  for (i=0; i < s->winsize; i++) {
330    s->in[i] = input->data[i];
331  }
332#else
333  memcpy(s->in, input->data, s->winsize * sizeof(smpl_t));
334#endif /* HAVE_MEMCPY_HACKS */
335
336#ifdef HAVE_FFTW3             // using FFTW3
337  fftw_execute(s->pfw);
338#ifdef HAVE_COMPLEX_H
339  compspec->data[0] = REAL(s->specdata[0]);
340  for (i = 1; i < s->fft_size -1 ; i++) {
341    compspec->data[i] = REAL(s->specdata[i]);
342    compspec->data[compspec->length - i] = IMAG(s->specdata[i]);
343  }
344  compspec->data[s->fft_size-1] = REAL(s->specdata[s->fft_size-1]);
345#else /* HAVE_COMPLEX_H  */
346  for (i = 0; i < s->fft_size; i++) {
347    compspec->data[i] = s->specdata[i];
348  }
349#endif /* HAVE_COMPLEX_H */
350
351#elif defined HAVE_ACCELERATE // using ACCELERATE
352  // convert real data to even/odd format used in vDSP
353  aubio_vDSP_ctoz((aubio_DSPComplex*)s->in, 2, &s->spec, 1, s->fft_size/2);
354  // compute the FFT
355  aubio_vDSP_fft_zrip(s->fftSetup, &s->spec, 1, s->log2fftsize, FFT_FORWARD);
356  // convert from vDSP complex split to [ r0, r1, ..., rN, iN-1, .., i2, i1]
357  compspec->data[0] = s->spec.realp[0];
358  compspec->data[s->fft_size / 2] = s->spec.imagp[0];
359  for (i = 1; i < s->fft_size / 2; i++) {
360    compspec->data[i] = s->spec.realp[i];
361    compspec->data[s->fft_size - i] = s->spec.imagp[i];
362  }
363  // apply scaling
364  smpl_t scale = 1./2.;
365  aubio_vDSP_vsmul(compspec->data, 1, &scale, compspec->data, 1, s->fft_size);
366
367#elif defined HAVE_INTEL_IPP  // using Intel IPP
368
369  // apply fft
370  aubio_ippsFFTFwd_RToCCS(s->in, (aubio_IppFloat*)s->complexOut, s->fftSpec, s->memBuffer);
371  // convert complex buffer to [ r0, r1, ..., rN, iN-1, .., i2, i1]
372  compspec->data[0] = s->complexOut[0].re;
373  compspec->data[s->fft_size / 2] = s->complexOut[s->fft_size / 2].re;
374  for (i = 1; i < s->fft_size / 2; i++) {
375    compspec->data[i] = s->complexOut[i].re;
376    compspec->data[s->fft_size - i] = s->complexOut[i].im;
377  }
378
379#else                         // using OOURA
380  aubio_ooura_rdft(s->winsize, 1, s->in, s->ip, s->w);
381  compspec->data[0] = s->in[0];
382  compspec->data[s->winsize / 2] = s->in[1];
383  for (i = 1; i < s->fft_size - 1; i++) {
384    compspec->data[i] = s->in[2 * i];
385    compspec->data[s->winsize - i] = - s->in[2 * i + 1];
386  }
387#endif /* using OOURA */
388}
389
390void aubio_fft_rdo_complex(aubio_fft_t * s, const fvec_t * compspec, fvec_t * output) {
391  uint_t i;
392#ifdef HAVE_FFTW3
393  const smpl_t renorm = 1./(smpl_t)s->winsize;
394#ifdef HAVE_COMPLEX_H
395  s->specdata[0] = compspec->data[0];
396  for (i=1; i < s->fft_size - 1; i++) {
397    s->specdata[i] = compspec->data[i] +
398      I * compspec->data[compspec->length - i];
399  }
400  s->specdata[s->fft_size - 1] = compspec->data[s->fft_size - 1];
401#else
402  for (i=0; i < s->fft_size; i++) {
403    s->specdata[i] = compspec->data[i];
404  }
405#endif
406  fftw_execute(s->pbw);
407  for (i = 0; i < output->length; i++) {
408    output->data[i] = s->out[i]*renorm;
409  }
410
411#elif defined HAVE_ACCELERATE // using ACCELERATE
412  // convert from real imag  [ r0, r1, ..., rN, iN-1, .., i2, i1]
413  // to vDSP packed format   [ r0, rN, r1, i1, ..., rN-1, iN-1 ]
414  s->out[0] = compspec->data[0];
415  s->out[1] = compspec->data[s->winsize / 2];
416  for (i = 1; i < s->fft_size / 2; i++) {
417    s->out[2 * i] = compspec->data[i];
418    s->out[2 * i + 1] = compspec->data[s->winsize - i];
419  }
420  // convert to split complex format used in vDSP
421  aubio_vDSP_ctoz((aubio_DSPComplex*)s->out, 2, &s->spec, 1, s->fft_size/2);
422  // compute the FFT
423  aubio_vDSP_fft_zrip(s->fftSetup, &s->spec, 1, s->log2fftsize, FFT_INVERSE);
424  // convert result to real output
425  aubio_vDSP_ztoc(&s->spec, 1, (aubio_DSPComplex*)output->data, 2, s->fft_size/2);
426  // apply scaling
427  smpl_t scale = 1.0 / s->winsize;
428  aubio_vDSP_vsmul(output->data, 1, &scale, output->data, 1, s->fft_size);
429
430#elif defined HAVE_INTEL_IPP  // using Intel IPP
431
432  // convert from real imag  [ r0, 0, ..., rN, iN-1, .., i2, i1, iN-1] to complex format
433  s->complexOut[0].re = compspec->data[0];
434  s->complexOut[0].im = 0;
435  s->complexOut[s->fft_size / 2].re = compspec->data[s->fft_size / 2];
436  s->complexOut[s->fft_size / 2].im = 0.0;
437  for (i = 1; i < s->fft_size / 2; i++) {
438    s->complexOut[i].re = compspec->data[i];
439    s->complexOut[i].im = compspec->data[s->fft_size - i];
440  }
441  // apply fft
442  aubio_ippsFFTInv_CCSToR((const aubio_IppFloat *)s->complexOut, output->data, s->fftSpec, s->memBuffer);
443  // apply scaling
444  aubio_ippsMulC(output->data, 1.0 / s->winsize, output->data, s->fft_size);
445
446#else                         // using OOURA
447  smpl_t scale = 2.0 / s->winsize;
448  s->out[0] = compspec->data[0];
449  s->out[1] = compspec->data[s->winsize / 2];
450  for (i = 1; i < s->fft_size - 1; i++) {
451    s->out[2 * i] = compspec->data[i];
452    s->out[2 * i + 1] = - compspec->data[s->winsize - i];
453  }
454  aubio_ooura_rdft(s->winsize, -1, s->out, s->ip, s->w);
455  for (i=0; i < s->winsize; i++) {
456    output->data[i] = s->out[i] * scale;
457  }
458#endif
459}
460
461void aubio_fft_get_spectrum(aubio_fft_t *s, const fvec_t * compspec, cvec_t * spectrum) {
462  aubio_fft_get_phas(s, compspec, spectrum);
463  aubio_fft_get_norm(s, compspec, spectrum);
464}
465
466void aubio_fft_get_realimag(aubio_fft_t *s, const cvec_t * spectrum, fvec_t * compspec) {
467  aubio_fft_get_imag(s, spectrum, compspec);
468  aubio_fft_get_real(s, spectrum, compspec);
469}
470
471void aubio_fft_get_phas(aubio_fft_t *s, const fvec_t * compspec, cvec_t * spectrum) {
472
473#ifdef INTEL_IPP_FFT // using Intel IPP FFT
474  uint_t i;
475
476  // convert from real imag  [ r0, 0, ..., rN, iN-1, .., i2, i1, iN-1] to complex format
477  s->complexOut[0].re = compspec->data[0];
478  s->complexOut[0].im = 0;
479  s->complexOut[s->fft_size / 2].re = compspec->data[s->fft_size / 2];
480  s->complexOut[s->fft_size / 2].im = 0.0;
481  for (i = 1; i < spectrum->length - 1; i++) {
482    s->complexOut[i].re = compspec->data[i];
483    s->complexOut[i].im = compspec->data[compspec->length - i];
484  }
485
486  IppStatus status = aubio_ippsPhas(s->complexOut, spectrum->phas, spectrum->length);
487  if (status != ippStsNoErr) {
488    AUBIO_ERR("fft: failed to extract phase from fft. IPP error: %d\n", status);
489  }
490
491#else                 // NOT using Intel IPP
492  uint_t i;
493  if (compspec->data[0] < 0) {
494    spectrum->phas[0] = PI;
495  } else {
496    spectrum->phas[0] = 0.;
497  }
498  for (i=1; i < spectrum->length - 1; i++) {
499    spectrum->phas[i] = ATAN2(compspec->data[compspec->length-i],
500        compspec->data[i]);
501  }
502  if (compspec->data[compspec->length/2] < 0) {
503    spectrum->phas[spectrum->length - 1] = PI;
504  } else {
505    spectrum->phas[spectrum->length - 1] = 0.;
506  }
507#endif
508}
509
510void aubio_fft_get_norm(aubio_fft_t *s, const fvec_t * compspec, cvec_t * spectrum) {
511  uint_t i = 0;
512  spectrum->norm[0] = ABS(compspec->data[0]);
513  for (i=1; i < spectrum->length - 1; i++) {
514    spectrum->norm[i] = SQRT(SQR(compspec->data[i])
515        + SQR(compspec->data[compspec->length - i]) );
516  }
517  spectrum->norm[spectrum->length-1] =
518    ABS(compspec->data[compspec->length/2]);
519}
520
521void aubio_fft_get_imag(aubio_fft_t *s, const cvec_t * spectrum, fvec_t * compspec) {
522  uint_t i;
523  for (i = 1; i < ( compspec->length + 1 ) / 2 /*- 1 + 1*/; i++) {
524    compspec->data[compspec->length - i] =
525      spectrum->norm[i]*SIN(spectrum->phas[i]);
526  }
527}
528
529void aubio_fft_get_real(aubio_fft_t *s, const cvec_t * spectrum, fvec_t * compspec) {
530  uint_t i;
531  for (i = 0; i < compspec->length / 2 + 1; i++) {
532    compspec->data[i] =
533      spectrum->norm[i]*COS(spectrum->phas[i]);
534  }
535}
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