ref: 965ea78a7a4aefa68e54f7c108e635740ed8b0fb
dir: /src/mathutils.c/
/*
Copyright (C) 2003-2009 Paul Brossier <piem@aubio.org>
This file is part of aubio.
aubio 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 3 of the License, or
(at your option) any later version.
aubio 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 aubio. If not, see <http://www.gnu.org/licenses/>.
*/
/* see in mathutils.h for doc */
#include "aubio_priv.h"
#include "fvec.h"
#include "mathutils.h"
#include "musicutils.h"
#include "config.h"
/** Window types */
typedef enum
{
aubio_win_rectangle,
aubio_win_hamming,
aubio_win_hanning,
aubio_win_hanningz,
aubio_win_blackman,
aubio_win_blackman_harris,
aubio_win_gaussian,
aubio_win_welch,
aubio_win_parzen,
aubio_win_default = aubio_win_hanningz,
} aubio_window_type;
fvec_t *
new_aubio_window (char_t * window_type, uint_t size)
{
// create fvec of size x 1 channel
fvec_t * win = new_fvec( size, 1);
smpl_t * w = win->data[0];
uint_t i;
aubio_window_type wintype;
if (strcmp (window_type, "rectangle") == 0)
wintype = aubio_win_rectangle;
else if (strcmp (window_type, "hamming") == 0)
wintype = aubio_win_hamming;
else if (strcmp (window_type, "hanning") == 0)
wintype = aubio_win_hanning;
else if (strcmp (window_type, "hanningz") == 0)
wintype = aubio_win_hanningz;
else if (strcmp (window_type, "blackman") == 0)
wintype = aubio_win_blackman;
else if (strcmp (window_type, "blackman_harris") == 0)
wintype = aubio_win_blackman_harris;
else if (strcmp (window_type, "gaussian") == 0)
wintype = aubio_win_gaussian;
else if (strcmp (window_type, "welch") == 0)
wintype = aubio_win_welch;
else if (strcmp (window_type, "parzen") == 0)
wintype = aubio_win_parzen;
else if (strcmp (window_type, "default") == 0)
wintype = aubio_win_default;
else {
AUBIO_ERR ("unknown window type %s, using default.\n", window_type);
wintype = aubio_win_default;
return NULL;
}
switch(wintype) {
case aubio_win_rectangle:
for (i=0;i<size;i++)
w[i] = 0.5;
break;
case aubio_win_hamming:
for (i=0;i<size;i++)
w[i] = 0.54 - 0.46 * COS(TWO_PI * i / (size));
break;
case aubio_win_hanning:
for (i=0;i<size;i++)
w[i] = 0.5 - (0.5 * COS(TWO_PI * i / (size)));
break;
case aubio_win_hanningz:
for (i=0;i<size;i++)
w[i] = 0.5 * (1.0 - COS(TWO_PI * i / (size)));
break;
case aubio_win_blackman:
for (i=0;i<size;i++)
w[i] = 0.42
- 0.50 * COS( TWO_PI*i/(size-1.0))
+ 0.08 * COS(2.0*TWO_PI*i/(size-1.0));
break;
case aubio_win_blackman_harris:
for (i=0;i<size;i++)
w[i] = 0.35875
- 0.48829 * COS( TWO_PI*i/(size-1.0))
+ 0.14128 * COS(2.0*TWO_PI*i/(size-1.0))
- 0.01168 * COS(3.0*TWO_PI*i/(size-1.0));
break;
case aubio_win_gaussian:
for (i=0;i<size;i++)
w[i] = EXP(- 1.0 / SQR(size) * SQR(2.0*i-size));
break;
case aubio_win_welch:
for (i=0;i<size;i++)
w[i] = 1.0 - SQR((2*i-size)/(size+1.0));
break;
case aubio_win_parzen:
for (i=0;i<size;i++)
w[i] = 1.0 - ABS((2*i-size)/(size+1.0));
break;
default:
break;
}
return win;
}
smpl_t
aubio_unwrap2pi (smpl_t phase)
{
/* mod(phase+pi,-2pi)+pi */
return phase + TWO_PI * (1. + FLOOR (-(phase + PI) / TWO_PI));
}
smpl_t
fvec_mean (fvec_t * s)
{
uint_t i, j;
smpl_t tmp = 0.0;
for (i = 0; i < s->channels; i++)
for (j = 0; j < s->length; j++)
tmp += s->data[i][j];
return tmp / (smpl_t) (s->length);
}
smpl_t
fvec_mean_channel (fvec_t * s, uint_t i)
{
uint_t j;
smpl_t tmp = 0.0;
for (j = 0; j < s->length; j++)
tmp += s->data[i][j];
return tmp / (smpl_t) (s->length);
}
smpl_t
fvec_sum (fvec_t * s)
{
uint_t i, j;
smpl_t tmp = 0.0;
for (i = 0; i < s->channels; i++) {
for (j = 0; j < s->length; j++) {
tmp += s->data[i][j];
}
}
return tmp;
}
smpl_t
fvec_max (fvec_t * s)
{
uint_t i, j;
smpl_t tmp = 0.0;
for (i = 0; i < s->channels; i++) {
for (j = 0; j < s->length; j++) {
tmp = (tmp > s->data[i][j]) ? tmp : s->data[i][j];
}
}
return tmp;
}
smpl_t
fvec_min (fvec_t * s)
{
uint_t i, j;
smpl_t tmp = s->data[0][0];
for (i = 0; i < s->channels; i++) {
for (j = 0; j < s->length; j++) {
tmp = (tmp < s->data[i][j]) ? tmp : s->data[i][j];
}
}
return tmp;
}
uint_t
fvec_min_elem (fvec_t * s)
{
uint_t i, j, pos = 0.;
smpl_t tmp = s->data[0][0];
for (i = 0; i < s->channels; i++) {
for (j = 0; j < s->length; j++) {
pos = (tmp < s->data[i][j]) ? pos : j;
tmp = (tmp < s->data[i][j]) ? tmp : s->data[i][j];
}
}
return pos;
}
uint_t
fvec_max_elem (fvec_t * s)
{
uint_t i, j, pos = 0;
smpl_t tmp = 0.0;
for (i = 0; i < s->channels; i++) {
for (j = 0; j < s->length; j++) {
pos = (tmp > s->data[i][j]) ? pos : j;
tmp = (tmp > s->data[i][j]) ? tmp : s->data[i][j];
}
}
return pos;
}
void
fvec_shift (fvec_t * s)
{
uint_t i, j;
for (i = 0; i < s->channels; i++) {
for (j = 0; j < s->length / 2; j++) {
ELEM_SWAP (s->data[i][j], s->data[i][j + s->length / 2]);
}
}
}
smpl_t
fvec_local_energy (fvec_t * f)
{
smpl_t energy = 0.;
uint_t i, j;
for (i = 0; i < f->channels; i++) {
for (j = 0; j < f->length; j++) {
energy += SQR (f->data[i][j]);
}
}
return energy;
}
smpl_t
fvec_local_hfc (fvec_t * v)
{
smpl_t hfc = 0.;
uint_t i, j;
for (i = 0; i < v->channels; i++) {
for (j = 0; j < v->length; j++) {
hfc += (i + 1) * v->data[i][j];
}
}
return hfc;
}
void
fvec_min_removal (fvec_t * v)
{
smpl_t v_min = fvec_min (v);
fvec_add (v, - v_min );
}
smpl_t
fvec_alpha_norm (fvec_t * o, smpl_t alpha)
{
uint_t i, j;
smpl_t tmp = 0.;
for (i = 0; i < o->channels; i++) {
for (j = 0; j < o->length; j++) {
tmp += POW (ABS (o->data[i][j]), alpha);
}
}
return POW (tmp / o->length, 1. / alpha);
}
void
fvec_alpha_normalise (fvec_t * o, smpl_t alpha)
{
uint_t i, j;
smpl_t norm = fvec_alpha_norm (o, alpha);
for (i = 0; i < o->channels; i++) {
for (j = 0; j < o->length; j++) {
o->data[i][j] /= norm;
}
}
}
void
fvec_add (fvec_t * o, smpl_t val)
{
uint_t i, j;
for (i = 0; i < o->channels; i++) {
for (j = 0; j < o->length; j++) {
o->data[i][j] += val;
}
}
}
void fvec_adapt_thres(fvec_t * vec, fvec_t * tmp,
uint_t post, uint_t pre, uint_t channel) {
uint_t length = vec->length, i=channel, j;
for (j=0;j<length;j++) {
vec->data[i][j] -= fvec_moving_thres(vec, tmp, post, pre, j, i);
}
}
smpl_t
fvec_moving_thres (fvec_t * vec, fvec_t * tmpvec,
uint_t post, uint_t pre, uint_t pos, uint_t channel)
{
uint_t i = channel, k;
smpl_t *medar = (smpl_t *) tmpvec->data[i];
uint_t win_length = post + pre + 1;
uint_t length = vec->length;
/* post part of the buffer does not exist */
if (pos < post + 1) {
for (k = 0; k < post + 1 - pos; k++)
medar[k] = 0.; /* 0-padding at the beginning */
for (k = post + 1 - pos; k < win_length; k++)
medar[k] = vec->data[0][k + pos - post];
/* the buffer is fully defined */
} else if (pos + pre < length) {
for (k = 0; k < win_length; k++)
medar[k] = vec->data[0][k + pos - post];
/* pre part of the buffer does not exist */
} else {
for (k = 0; k < length - pos + post; k++)
medar[k] = vec->data[0][k + pos - post];
for (k = length - pos + post; k < win_length; k++)
medar[k] = 0.; /* 0-padding at the end */
}
return fvec_median_channel (tmpvec, i);
}
smpl_t fvec_median_channel (fvec_t * input, uint_t channel) {
uint_t n = input->length;
smpl_t * arr = (smpl_t *) input->data[channel];
uint_t low, high ;
uint_t median;
uint_t middle, ll, hh;
low = 0 ; high = n-1 ; median = (low + high) / 2;
for (;;) {
if (high <= low) /* One element only */
return arr[median] ;
if (high == low + 1) { /* Two elements only */
if (arr[low] > arr[high])
ELEM_SWAP(arr[low], arr[high]) ;
return arr[median] ;
}
/* Find median of low, middle and high items; swap into position low */
middle = (low + high) / 2;
if (arr[middle] > arr[high]) ELEM_SWAP(arr[middle], arr[high]);
if (arr[low] > arr[high]) ELEM_SWAP(arr[low], arr[high]);
if (arr[middle] > arr[low]) ELEM_SWAP(arr[middle], arr[low]) ;
/* Swap low item (now in position middle) into position (low+1) */
ELEM_SWAP(arr[middle], arr[low+1]) ;
/* Nibble from each end towards middle, swapping items when stuck */
ll = low + 1;
hh = high;
for (;;) {
do ll++; while (arr[low] > arr[ll]) ;
do hh--; while (arr[hh] > arr[low]) ;
if (hh < ll)
break;
ELEM_SWAP(arr[ll], arr[hh]) ;
}
/* Swap middle item (in position low) back into correct position */
ELEM_SWAP(arr[low], arr[hh]) ;
/* Re-set active partition */
if (hh <= median)
low = ll;
if (hh >= median)
high = hh - 1;
}
}
smpl_t fvec_quadint (fvec_t * x, uint_t pos, uint_t i) {
smpl_t s0, s1, s2;
uint_t x0 = (pos < 1) ? pos : pos - 1;
uint_t x2 = (pos + 1 < x->length) ? pos + 1 : pos;
if (x0 == pos) return (x->data[i][pos] <= x->data[i][x2]) ? pos : x2;
if (x2 == pos) return (x->data[i][pos] <= x->data[i][x0]) ? pos : x0;
s0 = x->data[i][x0];
s1 = x->data[i][pos];
s2 = x->data[i][x2];
return pos + 0.5 * (s2 - s0 ) / (s2 - 2.* s1 + s0);
}
uint_t fvec_peakpick(fvec_t * onset, uint_t pos) {
uint_t i=0, tmp=0;
/*for (i=0;i<onset->channels;i++)*/
tmp = (onset->data[i][pos] > onset->data[i][pos-1]
&& onset->data[i][pos] > onset->data[i][pos+1]
&& onset->data[i][pos] > 0.);
return tmp;
}
smpl_t
aubio_quadfrac (smpl_t s0, smpl_t s1, smpl_t s2, smpl_t pf)
{
smpl_t tmp =
s0 + (pf / 2.) * (pf * (s0 - 2. * s1 + s2) - 3. * s0 + 4. * s1 - s2);
return tmp;
}
smpl_t
aubio_freqtomidi (smpl_t freq)
{
/* log(freq/A-2)/log(2) */
smpl_t midi = freq / 6.875;
midi = LOG (midi) / 0.69314718055995;
midi *= 12;
midi -= 3;
return midi;
}
smpl_t
aubio_miditofreq (smpl_t midi)
{
smpl_t freq = (midi + 3.) / 12.;
freq = EXP (freq * 0.69314718055995);
freq *= 6.875;
return freq;
}
smpl_t
aubio_bintofreq (smpl_t bin, smpl_t samplerate, smpl_t fftsize)
{
smpl_t freq = samplerate / fftsize;
return freq * bin;
}
smpl_t
aubio_bintomidi (smpl_t bin, smpl_t samplerate, smpl_t fftsize)
{
smpl_t midi = aubio_bintofreq (bin, samplerate, fftsize);
return aubio_freqtomidi (midi);
}
smpl_t
aubio_freqtobin (smpl_t freq, smpl_t samplerate, smpl_t fftsize)
{
smpl_t bin = fftsize / samplerate;
return freq * bin;
}
smpl_t
aubio_miditobin (smpl_t midi, smpl_t samplerate, smpl_t fftsize)
{
smpl_t freq = aubio_miditofreq (midi);
return aubio_freqtobin (freq, samplerate, fftsize);
}
uint_t
aubio_is_power_of_two (uint_t a)
{
if ((a & (a - 1)) == 0) {
return 1;
} else {
return 0;
}
}
uint_t
aubio_next_power_of_two (uint_t a)
{
uint_t i;
a--;
for (i = 0; i < sizeof (uint_t) * CHAR_BIT; i++) {
a = a | a >> 1;
}
return a + 1;
}
smpl_t
aubio_db_spl (fvec_t * o)
{
smpl_t val = SQRT (fvec_local_energy (o));
val /= (smpl_t) o->length;
return LIN2DB (val);
}
uint_t
aubio_silence_detection (fvec_t * o, smpl_t threshold)
{
return (aubio_db_spl (o) < threshold);
}
smpl_t
aubio_level_detection (fvec_t * o, smpl_t threshold)
{
smpl_t db_spl = aubio_db_spl (o);
if (db_spl < threshold) {
return 1.;
} else {
return db_spl;
}
}
smpl_t
aubio_zero_crossing_rate (fvec_t * input)
{
uint_t i = 0, j;
uint_t zcr = 0;
for (j = 1; j < input->length; j++) {
// previous was strictly negative
if (input->data[i][j - 1] < 0.) {
// current is positive or null
if (input->data[i][j] >= 0.) {
zcr += 1;
}
// previous was positive or null
} else {
// current is strictly negative
if (input->data[i][j] < 0.) {
zcr += 1;
}
}
}
return zcr / (smpl_t) input->length;
}
void
aubio_autocorr (fvec_t * input, fvec_t * output)
{
uint_t i, j, k, length = input->length;
smpl_t *data, *acf;
smpl_t tmp = 0;
for (k = 0; k < input->channels; k++) {
data = input->data[k];
acf = output->data[k];
for (i = 0; i < length; i++) {
tmp = 0.;
for (j = i; j < length; j++) {
tmp += data[j - i] * data[j];
}
acf[i] = tmp / (smpl_t) (length - i);
}
}
}
void
aubio_cleanup (void)
{
#if HAVE_FFTW3
fftw_cleanup ();
#else
#if HAVE_FFTW3F
fftwf_cleanup ();
#endif
#endif
}