ref: cfb7fb7bf50e9b25e486d0d9a5c1cc75f1d4055d
dir: /src/tempo/beattracking.c/
/*
Copyright (C) 2005-2009 Matthew Davies and 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/>.
*/
#include "aubio_priv.h"
#include "fvec.h"
#include "mathutils.h"
#include "tempo/beattracking.h"
/** define to 1 to print out tracking difficulties */
#define AUBIO_BEAT_WARNINGS 0
uint_t fvec_gettimesig (fvec_t * acf, uint_t acflen, uint_t gp);
void aubio_beattracking_checkstate (aubio_beattracking_t * bt);
struct _aubio_beattracking_t
{
uint_t hop_size; /** length of one tempo detection function sample, in audio samples */
uint_t samplerate; /** samplerate of the original signal */
fvec_t *rwv; /** rayleigh weighting for beat period in general model */
fvec_t *dfwv; /** exponential weighting for beat alignment in general model */
fvec_t *gwv; /** gaussian weighting for beat period in context dependant model */
fvec_t *phwv; /** gaussian weighting for beat alignment in context dependant model */
fvec_t *dfrev; /** reversed onset detection function */
fvec_t *acf; /** vector for autocorrelation function (of current detection function frame) */
fvec_t *acfout; /** store result of passing acf through s.i.c.f.b. */
fvec_t *phout;
uint_t timesig; /** time signature of input, set to zero until context dependent model activated */
uint_t step;
uint_t rayparam; /** Rayleigh parameter */
smpl_t lastbeat;
sint_t counter;
uint_t flagstep;
smpl_t g_var;
smpl_t gp;
smpl_t bp;
smpl_t rp;
smpl_t rp1;
smpl_t rp2;
};
aubio_beattracking_t *
new_aubio_beattracking (uint_t winlen, uint_t hop_size, uint_t samplerate)
{
aubio_beattracking_t *p = AUBIO_NEW (aubio_beattracking_t);
uint_t i = 0;
/* default value for rayleigh weighting - sets preferred tempo to 120bpm */
smpl_t rayparam = 60. * samplerate / 120. / hop_size;
smpl_t dfwvnorm = EXP ((LOG (2.0) / rayparam) * (winlen + 2));
/* length over which beat period is found [128] */
uint_t laglen = winlen / 4;
/* step increment - both in detection function samples -i.e. 11.6ms or
* 1 onset frame [128] */
uint_t step = winlen / 4; /* 1.5 seconds */
p->hop_size = hop_size;
p->samplerate = samplerate;
p->lastbeat = 0;
p->counter = 0;
p->flagstep = 0;
p->g_var = 3.901; // constthresh empirically derived!
p->rp = 1;
p->gp = 0;
p->rayparam = rayparam;
p->step = step;
p->rwv = new_fvec (laglen);
p->gwv = new_fvec (laglen);
p->dfwv = new_fvec (winlen);
p->dfrev = new_fvec (winlen);
p->acf = new_fvec (winlen);
p->acfout = new_fvec (laglen);
p->phwv = new_fvec (2 * laglen);
p->phout = new_fvec (winlen);
p->timesig = 0;
/* exponential weighting, dfwv = 0.5 when i = 43 */
for (i = 0; i < winlen; i++) {
p->dfwv->data[i] = (EXP ((LOG (2.0) / rayparam) * (i + 1)))
/ dfwvnorm;
}
for (i = 0; i < (laglen); i++) {
p->rwv->data[i] = ((smpl_t) (i + 1.) / SQR ((smpl_t) rayparam)) *
EXP ((-SQR ((smpl_t) (i + 1.)) / (2. * SQR ((smpl_t) rayparam))));
}
return p;
}
void
del_aubio_beattracking (aubio_beattracking_t * p)
{
del_fvec (p->rwv);
del_fvec (p->gwv);
del_fvec (p->dfwv);
del_fvec (p->dfrev);
del_fvec (p->acf);
del_fvec (p->acfout);
del_fvec (p->phwv);
del_fvec (p->phout);
AUBIO_FREE (p);
}
void
aubio_beattracking_do (aubio_beattracking_t * bt, const fvec_t * dfframe,
fvec_t * output)
{
uint_t i, k;
uint_t step = bt->step;
uint_t laglen = bt->rwv->length;
uint_t winlen = bt->dfwv->length;
uint_t maxindex = 0;
//number of harmonics in shift invariant comb filterbank
uint_t numelem = 4;
smpl_t phase; // beat alignment (step - lastbeat)
smpl_t beat; // beat position
smpl_t bp; // beat period
uint_t a, b; // used to build shift invariant comb filterbank
uint_t kmax; // number of elements used to find beat phase
/* copy dfframe, apply detection function weighting, and revert */
fvec_copy (dfframe, bt->dfrev);
fvec_weight (bt->dfrev, bt->dfwv);
fvec_rev (bt->dfrev);
/* compute autocorrelation function */
aubio_autocorr (dfframe, bt->acf);
/* if timesig is unknown, use metrically unbiased version of filterbank */
if (!bt->timesig) {
numelem = 4;
} else {
numelem = bt->timesig;
}
/* first and last output values are left intentionally as zero */
fvec_zeros (bt->acfout);
/* compute shift invariant comb filterbank */
for (i = 1; i < laglen - 1; i++) {
for (a = 1; a <= numelem; a++) {
for (b = 1; b < 2 * a; b++) {
bt->acfout->data[i] += bt->acf->data[i * a + b - 1]
* 1. / (2. * a - 1.);
}
}
}
/* apply Rayleigh weight */
fvec_weight (bt->acfout, bt->rwv);
/* find non-zero Rayleigh period */
maxindex = fvec_max_elem (bt->acfout);
if (maxindex > 0 && maxindex < bt->acfout->length - 1) {
bt->rp = fvec_quadratic_peak_pos (bt->acfout, maxindex);
} else {
bt->rp = bt->rayparam;
}
/* activate biased filterbank */
aubio_beattracking_checkstate (bt);
#if 0 // debug metronome mode
bt->bp = 36.9142;
#endif
bp = bt->bp;
/* end of biased filterbank */
if (bp == 0) {
fvec_zeros(output);
return;
}
/* deliberate integer operation, could be set to 3 max eventually */
kmax = FLOOR (winlen / bp);
/* initialize output */
fvec_zeros (bt->phout);
for (i = 0; i < bp; i++) {
for (k = 0; k < kmax; k++) {
bt->phout->data[i] += bt->dfrev->data[i + (uint_t) ROUND (bp * k)];
}
}
fvec_weight (bt->phout, bt->phwv);
/* find Rayleigh period */
maxindex = fvec_max_elem (bt->phout);
if (maxindex >= winlen - 1) {
#if AUBIO_BEAT_WARNINGS
AUBIO_WRN ("no idea what this groove's phase is\n");
#endif /* AUBIO_BEAT_WARNINGS */
phase = step - bt->lastbeat;
} else {
phase = fvec_quadratic_peak_pos (bt->phout, maxindex);
}
/* take back one frame delay */
phase += 1.;
#if 0 // debug metronome mode
phase = step - bt->lastbeat;
#endif
/* reset output */
fvec_zeros (output);
i = 1;
beat = bp - phase;
// AUBIO_DBG ("bp: %f, phase: %f, lastbeat: %f, step: %d, winlen: %d\n",
// bp, phase, bt->lastbeat, step, winlen);
/* the next beat will be earlier than 60% of the tempo period
skip this one */
if ( ( step - bt->lastbeat - phase ) < -0.40 * bp ) {
#if AUBIO_BEAT_WARNINGS
AUBIO_WRN ("back off-beat error, skipping this beat\n");
#endif /* AUBIO_BEAT_WARNINGS */
beat += bp;
}
/* start counting the beats */
while (beat + bp < 0) {
beat += bp;
}
if (beat >= 0) {
//AUBIO_DBG ("beat: %d, %f, %f\n", i, bp, beat);
output->data[i] = beat;
i++;
}
while (beat + bp <= step) {
beat += bp;
//AUBIO_DBG ("beat: %d, %f, %f\n", i, bp, beat);
output->data[i] = beat;
i++;
}
bt->lastbeat = beat;
/* store the number of beats in this frame as the first element */
output->data[0] = i;
}
uint_t
fvec_gettimesig (fvec_t * acf, uint_t acflen, uint_t gp)
{
sint_t k = 0;
smpl_t three_energy = 0., four_energy = 0.;
if (gp < 2) return 4;
if (acflen > 6 * gp + 2) {
for (k = -2; k < 2; k++) {
three_energy += acf->data[3 * gp + k];
four_energy += acf->data[4 * gp + k];
}
} else {
/*Expanded to be more accurate in time sig estimation */
for (k = -2; k < 2; k++) {
three_energy += acf->data[3 * gp + k] + acf->data[6 * gp + k];
four_energy += acf->data[4 * gp + k] + acf->data[2 * gp + k];
}
}
return (three_energy > four_energy) ? 3 : 4;
}
void
aubio_beattracking_checkstate (aubio_beattracking_t * bt)
{
uint_t i, j, a, b;
uint_t flagconst = 0;
sint_t counter = bt->counter;
uint_t flagstep = bt->flagstep;
smpl_t gp = bt->gp;
smpl_t bp = bt->bp;
smpl_t rp = bt->rp;
smpl_t rp1 = bt->rp1;
smpl_t rp2 = bt->rp2;
uint_t laglen = bt->rwv->length;
uint_t acflen = bt->acf->length;
uint_t step = bt->step;
fvec_t *acf = bt->acf;
fvec_t *acfout = bt->acfout;
if (gp) {
// compute shift invariant comb filterbank
fvec_zeros (acfout);
for (i = 1; i < laglen - 1; i++) {
for (a = 1; a <= bt->timesig; a++) {
for (b = 1; b < 2 * a; b++) {
acfout->data[i] += acf->data[i * a + b - 1];
}
}
}
// since gp is set, gwv has been computed in previous checkstate
fvec_weight (acfout, bt->gwv);
gp = fvec_quadratic_peak_pos (acfout, fvec_max_elem (acfout));
} else {
//still only using general model
gp = 0;
}
//now look for step change - i.e. a difference between gp and rp that
// is greater than 2*constthresh - always true in first case, since gp = 0
if (counter == 0) {
if (ABS (gp - rp) > 2. * bt->g_var) {
flagstep = 1; // have observed step change.
counter = 3; // setup 3 frame counter
} else {
flagstep = 0;
}
}
//i.e. 3rd frame after flagstep initially set
if (counter == 1 && flagstep == 1) {
//check for consistency between previous beatperiod values
if (ABS (2 * rp - rp1 - rp2) < bt->g_var) {
//if true, can activate context dependent model
flagconst = 1;
counter = 0; // reset counter and flagstep
} else {
//if not consistent, then don't flag consistency!
flagconst = 0;
counter = 2; // let it look next time
}
} else if (counter > 0) {
//if counter doesn't = 1,
counter = counter - 1;
}
rp2 = rp1;
rp1 = rp;
if (flagconst) {
/* first run of new hypothesis */
gp = rp;
bt->timesig = fvec_gettimesig (acf, acflen, gp);
for (j = 0; j < laglen; j++)
bt->gwv->data[j] =
EXP (-.5 * SQR ((smpl_t) (j + 1. - gp)) / SQR (bt->g_var));
flagconst = 0;
bp = gp;
/* flat phase weighting */
fvec_ones (bt->phwv);
} else if (bt->timesig) {
/* context dependant model */
bp = gp;
/* gaussian phase weighting */
if (step > bt->lastbeat) {
for (j = 0; j < 2 * laglen; j++) {
bt->phwv->data[j] =
EXP (-.5 * SQR ((smpl_t) (1. + j - step +
bt->lastbeat)) / (bp / 8.));
}
} else {
//AUBIO_DBG("NOT using phase weighting as step is %d and lastbeat %d \n",
// step,bt->lastbeat);
fvec_ones (bt->phwv);
}
} else {
/* initial state */
bp = rp;
/* flat phase weighting */
fvec_ones (bt->phwv);
}
/* do some further checks on the final bp value */
/* if tempo is > 206 bpm, half it */
while (0 < bp && bp < 25) {
#if AUBIO_BEAT_WARNINGS
AUBIO_WRN ("doubling from %f (%f bpm) to %f (%f bpm)\n",
bp, 60.*44100./512./bp, bp/2., 60.*44100./512./bp/2. );
//AUBIO_DBG("warning, halving the tempo from %f\n", 60.*samplerate/hopsize/bp);
#endif /* AUBIO_BEAT_WARNINGS */
bp = bp * 2;
}
//AUBIO_DBG("tempo:\t%3.5f bpm | ", 5168./bp);
/* smoothing */
//bp = (uint_t) (0.8 * (smpl_t)bp + 0.2 * (smpl_t)bp2);
//AUBIO_DBG("tempo:\t%3.5f bpm smoothed | bp2 %d | bp %d | ", 5168./bp, bp2, bp);
//bp2 = bp;
//AUBIO_DBG("time signature: %d \n", bt->timesig);
bt->counter = counter;
bt->flagstep = flagstep;
bt->gp = gp;
bt->bp = bp;
bt->rp1 = rp1;
bt->rp2 = rp2;
}
smpl_t
aubio_beattracking_get_period (const aubio_beattracking_t * bt)
{
return bt->hop_size * bt->bp;
}
smpl_t
aubio_beattracking_get_period_s (const aubio_beattracking_t * bt)
{
return aubio_beattracking_get_period(bt) / (smpl_t) bt->samplerate;
}
smpl_t
aubio_beattracking_get_bpm (const aubio_beattracking_t * bt)
{
if (bt->bp != 0) {
return 60. / aubio_beattracking_get_period_s(bt);
} else {
return 0.;
}
}
smpl_t
aubio_beattracking_get_confidence (const aubio_beattracking_t * bt)
{
if (bt->gp) {
smpl_t acf_sum = fvec_sum(bt->acfout);
if (acf_sum != 0.) {
return fvec_quadratic_peak_mag (bt->acfout, bt->gp) / acf_sum;
}
}
return 0.;
}