source: src/spectral/fft.c @ b701179

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Last change on this file since b701179 was b701179, checked in by Paul Brossier <piem@piem.org>, 3 years ago

src/*.c, wscript: remove trailing spaces

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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_ippsMalloc_complex       ippsMalloc_32fc
121#define aubio_ippsFFTInit_R            ippsFFTInit_R_32f
122#define aubio_ippsFFTGetSize_R         ippsFFTGetSize_R_32f
123#define aubio_ippsFFTInv_CCSToR        ippsFFTInv_CCSToR_32f
124#define aubio_ippsFFTFwd_RToCCS        ippsFFTFwd_RToCCS_32f
125#define aubio_ippsAtan2                ippsAtan2_32f_A21
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_ippsMalloc_complex       ippsMalloc_64fc
131#define aubio_ippsFFTInit_R            ippsFFTInit_R_64f
132#define aubio_ippsFFTGetSize_R         ippsFFTGetSize_R_64f
133#define aubio_ippsFFTInv_CCSToR        ippsFFTInv_CCSToR_64f
134#define aubio_ippsFFTFwd_RToCCS        ippsFFTFwd_RToCCS_64f
135#define aubio_ippsAtan2                ippsAtan2_64f_A50
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  smpl_t *in, *out;
162  Ipp8u* memSpec;
163  Ipp8u* memInit;
164  Ipp8u* memBuffer;
165  struct aubio_FFTSpec* fftSpec;
166  aubio_IppComplex* complexOut;
167#else                         // using OOURA
168  smpl_t *in, *out;
169  smpl_t *w;
170  int *ip;
171#endif /* using OOURA */
172
173  fvec_t * compspec;
174};
175
176aubio_fft_t * new_aubio_fft (uint_t winsize) {
177  aubio_fft_t * s = AUBIO_NEW(aubio_fft_t);
178  if ((sint_t)winsize < 2) {
179    AUBIO_ERR("fft: got winsize %d, but can not be < 2\n", winsize);
180    goto beach;
181  }
182
183#ifdef HAVE_FFTW3
184  uint_t i;
185  s->winsize  = winsize;
186  /* allocate memory */
187  s->in       = AUBIO_ARRAY(real_t,winsize);
188  s->out      = AUBIO_ARRAY(real_t,winsize);
189  s->compspec = new_fvec(winsize);
190  /* create plans */
191  pthread_mutex_lock(&aubio_fftw_mutex);
192#ifdef HAVE_COMPLEX_H
193  s->fft_size = winsize/2 + 1;
194  s->specdata = (fft_data_t*)fftw_malloc(sizeof(fft_data_t)*s->fft_size);
195  s->pfw = fftw_plan_dft_r2c_1d(winsize, s->in,  s->specdata, FFTW_ESTIMATE);
196  s->pbw = fftw_plan_dft_c2r_1d(winsize, s->specdata, s->out, FFTW_ESTIMATE);
197#else
198  s->fft_size = winsize;
199  s->specdata = (fft_data_t*)fftw_malloc(sizeof(fft_data_t)*s->fft_size);
200  s->pfw = fftw_plan_r2r_1d(winsize, s->in,  s->specdata, FFTW_R2HC, FFTW_ESTIMATE);
201  s->pbw = fftw_plan_r2r_1d(winsize, s->specdata, s->out, FFTW_HC2R, FFTW_ESTIMATE);
202#endif
203  pthread_mutex_unlock(&aubio_fftw_mutex);
204  for (i = 0; i < s->winsize; i++) {
205    s->in[i] = 0.;
206    s->out[i] = 0.;
207  }
208  for (i = 0; i < s->fft_size; i++) {
209    s->specdata[i] = 0.;
210  }
211
212#elif defined HAVE_ACCELERATE  // using ACCELERATE
213  s->winsize = winsize;
214  s->fft_size = winsize;
215  s->compspec = new_fvec(winsize);
216  s->log2fftsize = aubio_power_of_two_order(s->fft_size);
217  s->in = AUBIO_ARRAY(smpl_t, s->fft_size);
218  s->out = AUBIO_ARRAY(smpl_t, s->fft_size);
219  s->spec.realp = AUBIO_ARRAY(smpl_t, s->fft_size/2);
220  s->spec.imagp = AUBIO_ARRAY(smpl_t, s->fft_size/2);
221  s->fftSetup = aubio_vDSP_create_fftsetup(s->log2fftsize, FFT_RADIX2);
222
223#elif defined HAVE_INTEL_IPP  // using Intel IPP
224  const IppHintAlgorithm qualityHint = ippAlgHintAccurate; // OR ippAlgHintFast;
225  const int flags = IPP_FFT_NODIV_BY_ANY; // we're scaling manually afterwards
226  int order = aubio_power_of_two_order(winsize);
227  int sizeSpec, sizeInit, sizeBuffer;
228  IppStatus status;
229
230  if (winsize <= 4 || aubio_is_power_of_two(winsize) != 1)
231  {
232    AUBIO_ERR("intel IPP fft: can only create with sizes > 4 and power of two, requested %d,"
233      " try recompiling aubio with --enable-fftw3\n", winsize);
234    goto beach;
235  }
236
237  status = aubio_ippsFFTGetSize_R(order, flags, qualityHint,
238      &sizeSpec, &sizeInit, &sizeBuffer);
239  if (status != ippStsNoErr) {
240    AUBIO_ERR("fft: failed to initialize fft. IPP error: %d\n", status);
241    goto beach;
242  }
243  s->fft_size = s->winsize = winsize;
244  s->compspec = new_fvec(winsize);
245  s->in = AUBIO_ARRAY(smpl_t, s->winsize);
246  s->out = AUBIO_ARRAY(smpl_t, s->winsize);
247  s->memSpec = ippsMalloc_8u(sizeSpec);
248  s->memBuffer = ippsMalloc_8u(sizeBuffer);
249  if (sizeInit > 0 ) {
250    s->memInit = ippsMalloc_8u(sizeInit);
251  }
252  s->complexOut = aubio_ippsMalloc_complex(s->fft_size / 2 + 1);
253  status = aubio_ippsFFTInit_R(
254    &s->fftSpec, order, flags, qualityHint, s->memSpec, s->memInit);
255  if (status != ippStsNoErr) {
256    AUBIO_ERR("fft: failed to initialize. IPP error: %d\n", status);
257    goto beach;
258  }
259
260#else                         // using OOURA
261  if (aubio_is_power_of_two(winsize) != 1) {
262    AUBIO_ERR("fft: can only create with sizes power of two, requested %d,"
263        " try recompiling aubio with --enable-fftw3\n", winsize);
264    goto beach;
265  }
266  s->winsize = winsize;
267  s->fft_size = winsize / 2 + 1;
268  s->compspec = new_fvec(winsize);
269  s->in    = AUBIO_ARRAY(smpl_t, s->winsize);
270  s->out   = AUBIO_ARRAY(smpl_t, s->winsize);
271  s->ip    = AUBIO_ARRAY(int   , s->fft_size);
272  s->w     = AUBIO_ARRAY(smpl_t, s->fft_size);
273  s->ip[0] = 0;
274#endif /* using OOURA */
275
276  return s;
277
278beach:
279  AUBIO_FREE(s);
280  return NULL;
281}
282
283void del_aubio_fft(aubio_fft_t * s) {
284  /* destroy data */
285#ifdef HAVE_FFTW3             // using FFTW3
286  pthread_mutex_lock(&aubio_fftw_mutex);
287  fftw_destroy_plan(s->pfw);
288  fftw_destroy_plan(s->pbw);
289  fftw_free(s->specdata);
290  pthread_mutex_unlock(&aubio_fftw_mutex);
291
292#elif defined HAVE_ACCELERATE // using ACCELERATE
293  AUBIO_FREE(s->spec.realp);
294  AUBIO_FREE(s->spec.imagp);
295  aubio_vDSP_destroy_fftsetup(s->fftSetup);
296
297#elif defined HAVE_INTEL_IPP  // using Intel IPP
298  ippFree(s->memSpec);
299  ippFree(s->memInit);
300  ippFree(s->memBuffer);
301  ippFree(s->complexOut);
302
303#else                         // using OOURA
304  AUBIO_FREE(s->w);
305  AUBIO_FREE(s->ip);
306#endif
307
308  del_fvec(s->compspec);
309  AUBIO_FREE(s->in);
310  AUBIO_FREE(s->out);
311  AUBIO_FREE(s);
312}
313
314void aubio_fft_do(aubio_fft_t * s, const fvec_t * input, cvec_t * spectrum) {
315  aubio_fft_do_complex(s, input, s->compspec);
316  aubio_fft_get_spectrum(s->compspec, spectrum);
317}
318
319void aubio_fft_rdo(aubio_fft_t * s, const cvec_t * spectrum, fvec_t * output) {
320  aubio_fft_get_realimag(spectrum, s->compspec);
321  aubio_fft_rdo_complex(s, s->compspec, output);
322}
323
324void aubio_fft_do_complex(aubio_fft_t * s, const fvec_t * input, fvec_t * compspec) {
325  uint_t i;
326#ifndef HAVE_MEMCPY_HACKS
327  for (i=0; i < s->winsize; i++) {
328    s->in[i] = input->data[i];
329  }
330#else
331  memcpy(s->in, input->data, s->winsize * sizeof(smpl_t));
332#endif /* HAVE_MEMCPY_HACKS */
333
334#ifdef HAVE_FFTW3             // using FFTW3
335  fftw_execute(s->pfw);
336#ifdef HAVE_COMPLEX_H
337  compspec->data[0] = REAL(s->specdata[0]);
338  for (i = 1; i < s->fft_size -1 ; i++) {
339    compspec->data[i] = REAL(s->specdata[i]);
340    compspec->data[compspec->length - i] = IMAG(s->specdata[i]);
341  }
342  compspec->data[s->fft_size-1] = REAL(s->specdata[s->fft_size-1]);
343#else /* HAVE_COMPLEX_H  */
344  for (i = 0; i < s->fft_size; i++) {
345    compspec->data[i] = s->specdata[i];
346  }
347#endif /* HAVE_COMPLEX_H */
348
349#elif defined HAVE_ACCELERATE // using ACCELERATE
350  // convert real data to even/odd format used in vDSP
351  aubio_vDSP_ctoz((aubio_DSPComplex*)s->in, 2, &s->spec, 1, s->fft_size/2);
352  // compute the FFT
353  aubio_vDSP_fft_zrip(s->fftSetup, &s->spec, 1, s->log2fftsize, FFT_FORWARD);
354  // convert from vDSP complex split to [ r0, r1, ..., rN, iN-1, .., i2, i1]
355  compspec->data[0] = s->spec.realp[0];
356  compspec->data[s->fft_size / 2] = s->spec.imagp[0];
357  for (i = 1; i < s->fft_size / 2; i++) {
358    compspec->data[i] = s->spec.realp[i];
359    compspec->data[s->fft_size - i] = s->spec.imagp[i];
360  }
361  // apply scaling
362  smpl_t scale = 1./2.;
363  aubio_vDSP_vsmul(compspec->data, 1, &scale, compspec->data, 1, s->fft_size);
364
365#elif defined HAVE_INTEL_IPP  // using Intel IPP
366
367  // apply fft
368  aubio_ippsFFTFwd_RToCCS(s->in, (aubio_IppFloat*)s->complexOut, s->fftSpec, s->memBuffer);
369  // convert complex buffer to [ r0, r1, ..., rN, iN-1, .., i2, i1]
370  compspec->data[0] = s->complexOut[0].re;
371  compspec->data[s->fft_size / 2] = s->complexOut[s->fft_size / 2].re;
372  for (i = 1; i < s->fft_size / 2; i++) {
373    compspec->data[i] = s->complexOut[i].re;
374    compspec->data[s->fft_size - i] = s->complexOut[i].im;
375  }
376
377#else                         // using OOURA
378  aubio_ooura_rdft(s->winsize, 1, s->in, s->ip, s->w);
379  compspec->data[0] = s->in[0];
380  compspec->data[s->winsize / 2] = s->in[1];
381  for (i = 1; i < s->fft_size - 1; i++) {
382    compspec->data[i] = s->in[2 * i];
383    compspec->data[s->winsize - i] = - s->in[2 * i + 1];
384  }
385#endif /* using OOURA */
386}
387
388void aubio_fft_rdo_complex(aubio_fft_t * s, const fvec_t * compspec, fvec_t * output) {
389  uint_t i;
390#ifdef HAVE_FFTW3
391  const smpl_t renorm = 1./(smpl_t)s->winsize;
392#ifdef HAVE_COMPLEX_H
393  s->specdata[0] = compspec->data[0];
394  for (i=1; i < s->fft_size - 1; i++) {
395    s->specdata[i] = compspec->data[i] +
396      I * compspec->data[compspec->length - i];
397  }
398  s->specdata[s->fft_size - 1] = compspec->data[s->fft_size - 1];
399#else
400  for (i=0; i < s->fft_size; i++) {
401    s->specdata[i] = compspec->data[i];
402  }
403#endif
404  fftw_execute(s->pbw);
405  for (i = 0; i < output->length; i++) {
406    output->data[i] = s->out[i]*renorm;
407  }
408
409#elif defined HAVE_ACCELERATE // using ACCELERATE
410  // convert from real imag  [ r0, r1, ..., rN, iN-1, .., i2, i1]
411  // to vDSP packed format   [ r0, rN, r1, i1, ..., rN-1, iN-1 ]
412  s->out[0] = compspec->data[0];
413  s->out[1] = compspec->data[s->winsize / 2];
414  for (i = 1; i < s->fft_size / 2; i++) {
415    s->out[2 * i] = compspec->data[i];
416    s->out[2 * i + 1] = compspec->data[s->winsize - i];
417  }
418  // convert to split complex format used in vDSP
419  aubio_vDSP_ctoz((aubio_DSPComplex*)s->out, 2, &s->spec, 1, s->fft_size/2);
420  // compute the FFT
421  aubio_vDSP_fft_zrip(s->fftSetup, &s->spec, 1, s->log2fftsize, FFT_INVERSE);
422  // convert result to real output
423  aubio_vDSP_ztoc(&s->spec, 1, (aubio_DSPComplex*)output->data, 2, s->fft_size/2);
424  // apply scaling
425  smpl_t scale = 1.0 / s->winsize;
426  aubio_vDSP_vsmul(output->data, 1, &scale, output->data, 1, s->fft_size);
427
428#elif defined HAVE_INTEL_IPP  // using Intel IPP
429
430  // convert from real imag  [ r0, 0, ..., rN, iN-1, .., i2, i1, iN-1] to complex format
431  s->complexOut[0].re = compspec->data[0];
432  s->complexOut[0].im = 0;
433  s->complexOut[s->fft_size / 2].re = compspec->data[s->fft_size / 2];
434  s->complexOut[s->fft_size / 2].im = 0.0;
435  for (i = 1; i < s->fft_size / 2; i++) {
436    s->complexOut[i].re = compspec->data[i];
437    s->complexOut[i].im = compspec->data[s->fft_size - i];
438  }
439  // apply fft
440  aubio_ippsFFTInv_CCSToR((const aubio_IppFloat *)s->complexOut, output->data, s->fftSpec, s->memBuffer);
441  // apply scaling
442  aubio_ippsMulC(output->data, 1.0 / s->winsize, output->data, s->fft_size);
443
444#else                         // using OOURA
445  smpl_t scale = 2.0 / s->winsize;
446  s->out[0] = compspec->data[0];
447  s->out[1] = compspec->data[s->winsize / 2];
448  for (i = 1; i < s->fft_size - 1; i++) {
449    s->out[2 * i] = compspec->data[i];
450    s->out[2 * i + 1] = - compspec->data[s->winsize - i];
451  }
452  aubio_ooura_rdft(s->winsize, -1, s->out, s->ip, s->w);
453  for (i=0; i < s->winsize; i++) {
454    output->data[i] = s->out[i] * scale;
455  }
456#endif
457}
458
459void aubio_fft_get_spectrum(const fvec_t * compspec, cvec_t * spectrum) {
460  aubio_fft_get_phas(compspec, spectrum);
461  aubio_fft_get_norm(compspec, spectrum);
462}
463
464void aubio_fft_get_realimag(const cvec_t * spectrum, fvec_t * compspec) {
465  aubio_fft_get_imag(spectrum, compspec);
466  aubio_fft_get_real(spectrum, compspec);
467}
468
469void aubio_fft_get_phas(const fvec_t * compspec, cvec_t * spectrum) {
470  uint_t i;
471  if (compspec->data[0] < 0) {
472    spectrum->phas[0] = PI;
473  } else {
474    spectrum->phas[0] = 0.;
475  }
476#if defined(HAVE_INTEL_IPP)
477  // convert from real imag  [ r0, r1, ..., rN, iN-1, ..., i2, i1, i0]
478  //                     to  [ r0, r1, ..., rN, i0, i1, i2, ..., iN-1]
479  for (i = 1; i < spectrum->length / 2; i++) {
480    ELEM_SWAP(compspec->data[compspec->length - i],
481        compspec->data[spectrum->length + i - 1]);
482  }
483  aubio_ippsAtan2(compspec->data + spectrum->length,
484      compspec->data + 1, spectrum->phas + 1, spectrum->length - 1);
485  // revert the imaginary part back again
486  for (i = 1; i < spectrum->length / 2; i++) {
487    ELEM_SWAP(compspec->data[spectrum->length + i - 1],
488        compspec->data[compspec->length - i]);
489  }
490#else
491  for (i=1; i < spectrum->length - 1; i++) {
492    spectrum->phas[i] = ATAN2(compspec->data[compspec->length-i],
493        compspec->data[i]);
494  }
495#endif
496  if (compspec->data[compspec->length/2] < 0) {
497    spectrum->phas[spectrum->length - 1] = PI;
498  } else {
499    spectrum->phas[spectrum->length - 1] = 0.;
500  }
501}
502
503void aubio_fft_get_norm(const fvec_t * compspec, cvec_t * spectrum) {
504  uint_t i = 0;
505  spectrum->norm[0] = ABS(compspec->data[0]);
506  for (i=1; i < spectrum->length - 1; i++) {
507    spectrum->norm[i] = SQRT(SQR(compspec->data[i])
508        + SQR(compspec->data[compspec->length - i]) );
509  }
510  spectrum->norm[spectrum->length-1] =
511    ABS(compspec->data[compspec->length/2]);
512}
513
514void aubio_fft_get_imag(const cvec_t * spectrum, fvec_t * compspec) {
515  uint_t i;
516  for (i = 1; i < ( compspec->length + 1 ) / 2 /*- 1 + 1*/; i++) {
517    compspec->data[compspec->length - i] =
518      spectrum->norm[i]*SIN(spectrum->phas[i]);
519  }
520}
521
522void aubio_fft_get_real(const cvec_t * spectrum, fvec_t * compspec) {
523  uint_t i;
524  for (i = 0; i < compspec->length / 2 + 1; i++) {
525    compspec->data[i] =
526      spectrum->norm[i]*COS(spectrum->phas[i]);
527  }
528}
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