source: src/tempo/beattracking.c @ 3b2d32c

/*
         Copyright (C) 2005 Matthew Davies and Paul Brossier

         This program 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 2 of the License, or
         (at your option) any later version.

         This program 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 this program; if not, write to the Free Software
         Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
         
*/

#include "aubio_priv.h"
#include "fvec.h"
#include "mathutils.h"
#include "tempo/beattracking.h"

uint_t fvec_gettimesig(smpl_t * acf, uint_t acflen, uint_t gp);
void aubio_beattracking_checkstate(aubio_beattracking_t * bt);

struct _aubio_beattracking_t {
        fvec_t * rwv;    /** rayleigh weight vector - rayleigh distribution function */                    
        fvec_t * gwv;    /** rayleigh weight vector - rayleigh distribution function */                    
        fvec_t * dfwv;   /** detection function weighting - exponential curve */
        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 * phwv;   /** beat expectation alignment weighting */
        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 channels) {

        aubio_beattracking_t * p = AUBIO_NEW(aubio_beattracking_t);
        uint_t i        = 0;
        /* parameter for rayleigh weight vector - sets preferred tempo to
         * 120bpm [43] */
        smpl_t rayparam = 48./512. * winlen;
        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->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,channels);
        p->gwv     = new_fvec(laglen,channels);
        p->dfwv    = new_fvec(winlen,channels);
        p->dfrev   = new_fvec(winlen,channels);
        p->acf     = new_fvec(winlen,channels);
        p->acfout  = new_fvec(laglen,channels);
        p->phwv    = new_fvec(2*laglen,channels);
        p->phout   = new_fvec(winlen,channels);

        p->timesig = 0;

        /* exponential weighting, dfwv = 0.5 when i =  43 */
        for (i=0;i<winlen;i++) {
                p->dfwv->data[0][i] = (EXP((LOG(2.0)/rayparam)*(i+1)))
                        / dfwvnorm;
        } 

        for (i=0;i<(laglen);i++){
                p->rwv->data[0][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, 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;
        smpl_t * phout  = bt->phout->data[0];
        smpl_t * phwv   = bt->phwv->data[0];
        smpl_t * dfrev  = bt->dfrev->data[0];
        smpl_t * dfwv   = bt->dfwv->data[0];
        smpl_t * rwv    = bt->rwv->data[0];
        smpl_t * acfout = bt->acfout->data[0];
        smpl_t * acf    = bt->acf->data[0];
        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

        for (i = 0; i < winlen; i++){
                dfrev[winlen-1-i] = 0.;
                dfrev[winlen-1-i] = dfframe->data[0][i]*dfwv[i];
        }

        /* find 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 */
        for (i=0; i < bt->acfout->length; i++)
                acfout[i] = 0.;

        /* get acfout - assume Rayleigh weightvector only */
        for(i=1;i<laglen-1;i++){ 
                for (a=1; a<=numelem; a++){
                        for(b=(1-a); b<a; b++){
                                acfout[i] += acf[a*(i+1)+b-1] 
                                        * 1./(2.*a-1.)*rwv[i];
                        }
                }
        }

        /* find non-zero Rayleigh period */
        maxindex = vec_max_elem(bt->acfout);
        bt->rp = maxindex ? vec_quadint(bt->acfout, maxindex, 1) : 1;
        //rp = (maxindex==127) ? 43 : maxindex; //rayparam
        bt->rp = (maxindex==bt->acfout->length-1) ? bt->rayparam : maxindex; //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 */

        /* initialize output */
        for(i=0;i<bt->phout->length;i++)     {phout[i] = 0.;} 

        /* deliberate integer operation, could be set to 3 max eventually */
        kmax = FLOOR(winlen/bp);

        for(i=0;i<bp;i++){
                phout[i] = 0.;
                for(k=0;k<kmax;k++){
                        phout[i] += dfrev[i+(uint_t)ROUND(bp*k)] * phwv[i];
                }
        }

        /* find Rayleigh period */
        maxindex = vec_max_elem(bt->phout);
        if (maxindex == winlen) maxindex = 0;
        phase =  1. + vec_quadint(bt->phout, maxindex, 1);
#if 0 // debug metronome mode
        phase = step - bt->lastbeat;
#endif

        /* reset output */
        for (i = 0; i < laglen; i++)
                output->data[0][i] = 0.;

        i = 1;
        beat = bp - phase;
        /* start counting the beats */
        if(beat >= 0)
        {
                output->data[0][i] = beat;
                i++;
        }

        while( beat + bp <= step)
        {
                beat += bp;
                output->data[0][i] = beat;
                i++;
        }

        bt->lastbeat = beat;
        /* store the number of beat found in this frame as the first element */
        output->data[0][0] = i;
}

uint_t fvec_gettimesig(smpl_t * acf, uint_t acflen, uint_t gp){
        sint_t k = 0;
        smpl_t three_energy = 0., four_energy = 0.;
        if( acflen > 6 * gp + 2 ){
                for(k=-2;k<2;k++){
                        three_energy += acf[3*gp+k];
                        four_energy += acf[4*gp+k];
                }
        }
        else{ /*Expanded to be more accurate in time sig estimation*/
                for(k=-2;k<2;k++){
                        three_energy += acf[3*gp+k]+acf[6*gp+k];
                        four_energy += acf[4*gp+k]+acf[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;
        smpl_t * acf    = bt->acf->data[0];
        smpl_t * acfout = bt->acfout->data[0];
        smpl_t * gwv    = bt->gwv->data[0];
        smpl_t * phwv   = bt->phwv->data[0];

        if (gp) {
                // doshiftfbank again only if context dependent model is in operation
                //acfout = doshiftfbank(acf,gwv,timesig,laglen,acfout); 
                //don't need acfout now, so can reuse vector
                // gwv is, in first loop, definitely all zeros, but will have
                // proper values when context dependent model is activated
                for (i=0; i < bt->acfout->length; i++)
                       acfout[i] = 0.;
                for(i=1;i<laglen-1;i++){ 
                        for (a=1;a<=bt->timesig;a++){
                                for(b=(1-a);b<a;b++){
                                        acfout[i] += acf[a*(i+1)+b-1] 
                                                * 1. * gwv[i];
                                }
                        }
                }
                gp = vec_quadint(bt->acfout, vec_max_elem(bt->acfout), 1);
                /*
                while(gp<32) gp =gp*2;
                while(gp>64) gp = gp/2;
                */
        } 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++)
                        gwv[j] = EXP(-.5*SQR((smpl_t)(j+1.-gp))/SQR(bt->g_var));
                flagconst = 0;
                bp = gp;
                /* flat phase weighting */
                for(j=0;j<2*laglen;j++)  {phwv[j] = 1.;} 
        } else if (bt->timesig) {
                /* context dependant model */
                bp = gp;
                /* gaussian phase weighting */
                if (step > bt->lastbeat) {
                        for(j=0;j<2*laglen;j++)  {
                                phwv[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);
                        for(j=0;j<2*laglen;j++)  {phwv[j] = 1.;} 
                }
        } else {
                /* initial state */ 
                bp = rp;
                /* flat phase weighting */
                for(j=0;j<2*laglen;j++)  {phwv[j] = 1.;} 
        }

        /* do some further checks on the final bp value */

        /* if tempo is > 206 bpm, half it */
        while (bp < 25) {
                //AUBIO_DBG("warning, doubling the beat period from %d\n", bp);
                //AUBIO_DBG("warning, halving the tempo from %f\n", 60.*samplerate/hopsize/bp);
                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_bpm(aubio_beattracking_t * bt) {
        if (bt->timesig != 0 && bt->counter == 0 && bt->flagstep == 0) {
          return 5168. / vec_quadint(bt->acfout, bt->bp, 1);
        } else {
          return 0.;
        }
}

smpl_t aubio_beattracking_get_confidence(aubio_beattracking_t * bt) {
        if (bt->gp) return vec_max(bt->acfout);
        else return 0.;
}