c@277: /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
c@277: 
c@277: /*
c@277:     QM DSP Library
c@277: 
c@277:     Centre for Digital Music, Queen Mary, University of London.
c@277:     This file copyright 2008-2009 Matthew Davies and QMUL.
c@277:     All rights reserved.
c@277: */
c@277: 
c@277: #include "TempoTrackV2.h"
c@277: 
c@277: #include <cmath>
c@277: #include <cstdlib>
c@278: #include <iostream>
c@277: 
c@277: 
c@277: //#define		FRAMESIZE	512
c@277: //#define		BIGFRAMESIZE	1024
c@277: #define   TWOPI 6.283185307179586232
c@277: #define   EPS 0.0000008 // just some arbitrary small number
c@277: 
c@277: TempoTrackV2::TempoTrackV2() { }
c@277: TempoTrackV2::~TempoTrackV2() { }
c@277: 
c@277: void
c@277: TempoTrackV2::adapt_thresh(d_vec_t &df)
c@277: {
c@278:     d_vec_t smoothed(df.size());
c@278: 	
c@278:     int p_post = 7;
c@278:     int p_pre = 8;
c@277: 
c@278:     int t = std::min(static_cast<int>(df.size()),p_post);	// what is smaller, p_post of df size. This is to avoid accessing outside of arrays
c@277: 
c@278:     // find threshold for first 't' samples, where a full average cannot be computed yet 
c@278:     for (int i = 0;i <= t;i++)
c@278:     {	
c@278:         int k = std::min((i+p_pre),static_cast<int>(df.size()));
c@278:         smoothed[i] = mean_array(df,1,k);
c@278:     }
c@278:     // find threshold for bulk of samples across a moving average from [i-p_pre,i+p_post]
c@278:     for (uint i = t+1;i < df.size()-p_post;i++)
c@278:     {
c@278:         smoothed[i] = mean_array(df,i-p_pre,i+p_post);
c@278:     }
c@278:     // for last few samples calculate threshold, again, not enough samples to do as above
c@278:     for (uint i = df.size()-p_post;i < df.size();i++)
c@278:     {
c@278:         int k = std::max((static_cast<int> (i) -p_post),1);
c@278:         smoothed[i] = mean_array(df,k,df.size());
c@278:     }
c@277: 
c@278:     // subtract the threshold from the detection function and check that it is not less than 0
c@278:     for (uint i = 0;i < df.size();i++)
c@278:     {
c@278:         df[i] -= smoothed[i];
c@278:         if (df[i] < 0)
c@278:         {
c@278:             df[i] = 0;
c@278:         }
c@278:     }
c@277: }
c@277: 
c@277: double
c@277: TempoTrackV2::mean_array(const d_vec_t &dfin,int start,int end)
c@277: {
c@278:     double sum = 0.;
c@278: 	
c@278:     // find sum
c@278:     for (int i = start;i < end;i++)
c@278:     {
c@278:         sum += dfin[i];
c@278:     }
c@277: 
c@278:     return static_cast<double> (sum / (end - start + 1) );	// average and return
c@277: }
c@277: 
c@277: void
c@277: TempoTrackV2::filter_df(d_vec_t &df)
c@277: {
c@278:     d_vec_t a(3);
c@278:     d_vec_t b(3);
c@278:     d_vec_t	lp_df(df.size());
c@277: 
c@278:     //equivalent in matlab to [b,a] = butter(2,0.4);
c@278:     a[0] = 1.0000;
c@278:     a[1] = -0.3695;
c@278:     a[2] = 0.1958;
c@278:     b[0] = 0.2066;
c@278:     b[1] = 0.4131;
c@278:     b[2] = 0.2066;
c@278:     
c@278:     double inp1 = 0.;
c@278:     double inp2 = 0.;
c@278:     double out1 = 0.;
c@278:     double out2 = 0.;
c@277: 
c@277: 
c@278:     // forwards filtering
c@278:     for (uint i = 0;i < df.size();i++)
c@278:     {
c@278:         lp_df[i] =  b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
c@278:         inp2 = inp1;
c@278:         inp1 = df[i];
c@278:         out2 = out1;
c@278:         out1 = lp_df[i];
c@278:     }
c@277: 
c@278:     // copy forwards filtering to df...
c@278:     // but, time-reversed, ready for backwards filtering
c@278:     for (uint i = 0;i < df.size();i++)
c@278:     {
c@278:         df[i] = lp_df[df.size()-i-1];
c@278:     }
c@277: 
c@278:     for (uint i = 0;i < df.size();i++)
c@278:     {
c@278:         lp_df[i] = 0.;    
c@278:     }
c@277: 
c@278:     inp1 = 0.; inp2 = 0.;
c@278:     out1 = 0.; out2 = 0.;
c@277: 
c@277:   // backwards filetering on time-reversed df
c@278:     for (uint i = 0;i < df.size();i++)
c@278:     {
c@278:         lp_df[i] =  b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
c@278:         inp2 = inp1;
c@278:         inp1 = df[i];
c@278:         out2 = out1;
c@278:         out1 = lp_df[i];
c@278:     }
c@277: 
c@277:   // write the re-reversed (i.e. forward) version back to df
c@278:     for (uint i = 0;i < df.size();i++)
c@278:     {
c@278:         df[i] = lp_df[df.size()-i-1];
c@278:     }
c@277: }
c@277: 
c@277: 
c@277: void
c@278: TempoTrackV2::calculateBeatPeriod(const d_vec_t &df, d_vec_t &beat_period,
c@278:                                   d_vec_t &tempi)
c@277: {
c@278:     // to follow matlab.. split into 512 sample frames with a 128 hop size
c@278:     // calculate the acf,
c@278:     // then the rcf.. and then stick the rcfs as columns of a matrix
c@278:     // then call viterbi decoding with weight vector and transition matrix
c@278:     // and get best path
c@277: 
c@278:     uint wv_len = 128;
c@278:     double rayparam = 43.;
c@277: 
c@278:     // make rayleigh weighting curve
c@278:     d_vec_t wv(wv_len);
c@278:     for (uint i=0; i<wv.size(); i++)
c@277:     {
c@278:         wv[i] = (static_cast<double> (i) / pow(rayparam,2.)) * exp((-1.*pow(-static_cast<double> (i),2.)) / (2.*pow(rayparam,2.)));
c@277:     }
c@277: 
c@278:     // beat tracking frame size (roughly 6 seconds) and hop (1.5 seconds)
c@278:     uint winlen = 512;
c@278:     uint step = 128;
c@278: 
c@278:     // matrix to store output of comb filter bank, increment column of matrix at each frame
c@278:     d_mat_t rcfmat;
c@278:     int col_counter = -1;
c@278: 
c@278:     // main loop for beat period calculation
c@278:     for (uint i=0; i<(df.size()-winlen); i+=step)
c@278:     {
c@278:         // get dfframe
c@278:         d_vec_t dfframe(winlen);
c@278:         for (uint k=0; k<winlen; k++)
c@278:         {
c@278:             dfframe[k] = df[i+k];
c@278:         }
c@278:         // get rcf vector for current frame
c@278:         d_vec_t rcf(wv_len);    
c@278:         get_rcf(dfframe,wv,rcf);
c@277:   
c@278:         rcfmat.push_back( d_vec_t() ); // adds a new column
c@278:         col_counter++;
c@278:         for (uint j=0; j<rcf.size(); j++)
c@278:         {
c@278:             rcfmat[col_counter].push_back( rcf[j] );
c@278:         }
c@278:     }
c@278:   
c@278:     // now call viterbi decoding function
c@278:     viterbi_decode(rcfmat,wv,beat_period,tempi);
c@277: }
c@277: 
c@277: 
c@277: void
c@277: TempoTrackV2::get_rcf(const d_vec_t &dfframe_in, const d_vec_t &wv, d_vec_t &rcf)
c@277: {
c@278:     // calculate autocorrelation function
c@278:     // then rcf
c@278:     // just hard code for now... don't really need separate functions to do this
c@277: 
c@278:     // make acf
c@277: 
c@278:     d_vec_t dfframe(dfframe_in);
c@277: 
c@278:     adapt_thresh(dfframe);
c@277: 
c@278:     d_vec_t acf(dfframe.size());
c@277: 
c@278:     
c@278:     for (uint lag=0; lag<dfframe.size(); lag++)
c@278:     {
c@278:         double sum = 0.;
c@278:         double tmp = 0.;
c@277: 
c@278:         for (uint n=0; n<(dfframe.size()-lag); n++)
c@278:         {
c@278:             tmp = dfframe[n] * dfframe[n+lag];    
c@278:             sum += tmp;
c@278:         }
c@278:         acf[lag] = static_cast<double> (sum/ (dfframe.size()-lag));
c@278:     }
c@277: 
c@278:     // now apply comb filtering
c@278:     int numelem = 4;
c@278: 	
c@278:     for (uint i = 2;i < rcf.size();i++) // max beat period
c@278:     {
c@278:         for (int a = 1;a <= numelem;a++) // number of comb elements
c@278:         {
c@278:             for (int b = 1-a;b <= a-1;b++) // general state using normalisation of comb elements
c@278:             {
c@278:                 rcf[i-1] += ( acf[(a*i+b)-1]*wv[i-1] ) / (2.*a-1.);	// calculate value for comb filter row
c@278:             }
c@278:         }
c@278:     }
c@278:   
c@278:     // apply adaptive threshold to rcf
c@278:     adapt_thresh(rcf);
c@278:   
c@278:     double rcfsum =0.;
c@278:     for (uint i=0; i<rcf.size(); i++)
c@278:     {
c@278:         rcf[i] += EPS ;
c@278:         rcfsum += rcf[i];
c@278:     }
c@277: 
c@278:     // normalise rcf to sum to unity
c@278:     for (uint i=0; i<rcf.size(); i++)
c@277:     {
c@278:         rcf[i] /= (rcfsum + EPS);
c@277:     }
c@277: }
c@277: 
c@277: void
c@278: TempoTrackV2::viterbi_decode(const d_mat_t &rcfmat, const d_vec_t &wv, d_vec_t &beat_period, d_vec_t &tempi)
c@277: {
c@278:     // following Kevin Murphy's Viterbi decoding to get best path of
c@278:     // beat periods through rfcmat
c@277: 
c@278:     // make transition matrix
c@278:     d_mat_t tmat;
c@278:     for (uint i=0;i<wv.size();i++)
c@278:     {
c@278:         tmat.push_back ( d_vec_t() ); // adds a new column
c@278:         for (uint j=0; j<wv.size(); j++)
c@278:         {	
c@278:             tmat[i].push_back(0.); // fill with zeros initially
c@278:         }
c@278:     }
c@278:     
c@278:     // variance of Gaussians in transition matrix
c@278:     // formed of Gaussians on diagonal - implies slow tempo change
c@278:     double sigma = 8.;
c@278:     // don't want really short beat periods, or really long ones
c@278:     for (uint i=20;i <wv.size()-20; i++)
c@278:     {
c@278:         for (uint j=20; j<wv.size()-20; j++)
c@278:         {	
c@278:             double mu = static_cast<double>(i);
c@278:             tmat[i][j] = exp( (-1.*pow((j-mu),2.)) / (2.*pow(sigma,2.)) );
c@278:         }
c@278:     }
c@277: 
c@278:     // parameters for Viterbi decoding... this part is taken from
c@278:     // Murphy's matlab
c@277: 
c@278:     d_mat_t delta;
c@278:     i_mat_t psi;
c@278:     for (uint i=0;i <rcfmat.size(); i++)
c@278:     {
c@278:         delta.push_back( d_vec_t());
c@278:         psi.push_back( i_vec_t());
c@278:         for (uint j=0; j<rcfmat[i].size(); j++)
c@278:         {	
c@278:             delta[i].push_back(0.); // fill with zeros initially
c@278:             psi[i].push_back(0); // fill with zeros initially
c@278:         }
c@278:     }
c@277: 
c@277: 
c@278:     uint T = delta.size();
c@278:     uint Q = delta[0].size();
c@277: 
c@278:     // initialize first column of delta
c@277:     for (uint j=0; j<Q; j++)
c@277:     {
c@278:         delta[0][j] = wv[j] * rcfmat[0][j];
c@278:         psi[0][j] = 0;
c@277:     }
c@278:     
c@277:     double deltasum = 0.;
c@277:     for (uint i=0; i<Q; i++)
c@277:     {
c@278:         deltasum += delta[0][i];
c@277:     }      
c@277:     for (uint i=0; i<Q; i++)
c@277:     {
c@278:         delta[0][i] /= (deltasum + EPS);
c@277:     }      
c@277: 
c@277: 
c@278:     for (uint t=1; t<T; t++)
c@278:     {
c@278:         d_vec_t tmp_vec(Q);
c@277: 
c@278:         for (uint j=0; j<Q; j++)
c@278:         {
c@278:             for (uint i=0; i<Q; i++)
c@278:             {
c@278:                 tmp_vec[i] = delta[t-1][i] * tmat[j][i];
c@278:             }      
c@278:    
c@278:             delta[t][j] = get_max_val(tmp_vec);    
c@277: 
c@278:             psi[t][j] = get_max_ind(tmp_vec);
c@278:  
c@278:             delta[t][j] *= rcfmat[t][j];
c@278:         }
c@277: 
c@278:         // normalise current delta column
c@278:         double deltasum = 0.;
c@278:         for (uint i=0; i<Q; i++)
c@278:         {
c@278:             deltasum += delta[t][i];
c@278:         }      
c@278:         for (uint i=0; i<Q; i++)
c@278:         {
c@278:             delta[t][i] /= (deltasum + EPS);
c@278:         }      
c@278:     }
c@277: 
c@278:     i_vec_t bestpath(T);
c@278:     d_vec_t tmp_vec(Q);
c@278:     for (uint i=0; i<Q; i++)
c@278:     {  
c@278:         tmp_vec[i] = delta[T-1][i];
c@278:     }
c@277: 
c@278:     // find starting point - best beat period for "last" frame
c@278:     bestpath[T-1] = get_max_ind(tmp_vec);
c@278:  
c@278:     // backtrace through index of maximum values in psi
c@278:     for (uint t=T-2; t>0 ;t--)
c@278:     {
c@278:         bestpath[t] = psi[t+1][bestpath[t+1]];
c@278:     }
c@277: 
c@278:     // weird but necessary hack -- couldn't get above loop to terminate at t >= 0
c@278:     bestpath[0] = psi[1][bestpath[1]];
c@277: 
c@278:     uint lastind = 0;
c@278:     for (uint i=0; i<T; i++)
c@278:     {  
c@278:         uint step = 128;
c@278:         for (uint j=0; j<step; j++)
c@278:         {
c@278:             lastind = i*step+j;
c@278:             beat_period[lastind] = bestpath[i];
c@278:         }
c@278:     }
c@277: 
c@278:     //fill in the last values...
c@278:     for (uint i=lastind; i<beat_period.size(); i++)
c@278:     {
c@278:         beat_period[i] = beat_period[lastind];
c@278:     }
c@277: 
c@278:     for (uint i = 0; i < beat_period.size(); i++)
c@277:     {
c@278:         tempi.push_back((60.*44100./512.)/beat_period[i]);
c@277:     }
c@277: }
c@277: 
c@277: double
c@277: TempoTrackV2::get_max_val(const d_vec_t &df)
c@277: {
c@278:     double maxval = 0.;
c@278:     for (uint i=0; i<df.size(); i++)
c@277:     {
c@278:         if (maxval < df[i])
c@278:         {
c@278:             maxval = df[i];
c@278:         }
c@277:     }
c@277:     
c@278:     return maxval;
c@277: }
c@277: 
c@277: int
c@277: TempoTrackV2::get_max_ind(const d_vec_t &df)
c@277: {
c@278:     double maxval = 0.;
c@278:     int ind = 0;
c@278:     for (uint i=0; i<df.size(); i++)
c@277:     {
c@278:         if (maxval < df[i])
c@278:         {
c@278:             maxval = df[i];
c@278:             ind = i;
c@278:         }
c@277:     }
c@278:     
c@278:     return ind;
c@277: }
c@277: 
c@277: void
c@277: TempoTrackV2::normalise_vec(d_vec_t &df)
c@277: {
c@278:     double sum = 0.;
c@278:     for (uint i=0; i<df.size(); i++)
c@278:     {
c@278:         sum += df[i];
c@278:     }
c@278:     
c@278:     for (uint i=0; i<df.size(); i++)
c@278:     {
c@278:         df[i]/= (sum + EPS);
c@278:     }
c@277: }
c@277: 
c@277: void
c@277: TempoTrackV2::calculateBeats(const d_vec_t &df, const d_vec_t &beat_period,
c@277:                              d_vec_t &beats)
c@277: {
c@278:     d_vec_t cumscore(df.size()); // store cumulative score
c@278:     i_vec_t backlink(df.size()); // backlink (stores best beat locations at each time instant)
c@278:     d_vec_t localscore(df.size()); // localscore, for now this is the same as the detection function
c@277: 
c@278:     for (uint i=0; i<df.size(); i++)
c@277:     {
c@278:         localscore[i] = df[i];
c@278:         backlink[i] = -1;
c@277:     }
c@277: 
c@278:     double tightness = 4.;
c@278:     double alpha = 0.9;
c@277: 
c@278:     // main loop
c@278:     for (uint i=0; i<localscore.size(); i++)
c@278:     {
c@278:         int prange_min = -2*beat_period[i];
c@278:         int prange_max = round(-0.5*beat_period[i]);
c@277: 
c@278:         // transition range
c@278:         d_vec_t txwt (prange_max - prange_min + 1);
c@278:         d_vec_t scorecands (txwt.size());
c@277: 
c@278:         for (uint j=0;j<txwt.size();j++)
c@278:         {
c@278:             double mu = static_cast<double> (beat_period[i]);
c@278:             txwt[j] = exp( -0.5*pow(tightness * log((round(2*mu)-j)/mu),2));
c@277: 
c@278:             // IF IN THE ALLOWED RANGE, THEN LOOK AT CUMSCORE[I+PRANGE_MIN+J
c@278:             // ELSE LEAVE AT DEFAULT VALUE FROM INITIALISATION:  D_VEC_T SCORECANDS (TXWT.SIZE());
c@277: 
c@278:             int cscore_ind = i+prange_min+j;
c@278:             if (cscore_ind >= 0)   
c@278:             {
c@278:                 scorecands[j] = txwt[j] * cumscore[cscore_ind];
c@278:             }
c@278:         }
c@277: 
c@278:         // find max value and index of maximum value
c@278:         double vv = get_max_val(scorecands);
c@278:         int xx = get_max_ind(scorecands);
c@277: 
c@278:         cumscore[i] = alpha*vv + (1.-alpha)*localscore[i];
c@278:         backlink[i] = i+prange_min+xx;
c@278:     }
c@278: 
c@278:     // STARTING POINT, I.E. LAST BEAT.. PICK A STRONG POINT IN cumscore VECTOR
c@278:     d_vec_t tmp_vec;
c@278:     for (uint i=cumscore.size() - beat_period[beat_period.size()-1] ; i<cumscore.size(); i++)
c@278:     {
c@278:         tmp_vec.push_back(cumscore[i]);
c@278:     }  
c@278: 
c@278:     int startpoint = get_max_ind(tmp_vec) + cumscore.size() - beat_period[beat_period.size()-1] ;
c@278: 
c@278:     // USE BACKLINK TO GET EACH NEW BEAT (TOWARDS THE BEGINNING OF THE FILE)
c@278:     //  BACKTRACKING FROM THE END TO THE BEGINNING.. MAKING SURE NOT TO GO BEFORE SAMPLE 0
c@278:     i_vec_t ibeats;
c@278:     ibeats.push_back(startpoint);
c@278:     while (backlink[ibeats.back()] > 0)
c@278:     {
c@278:         ibeats.push_back(backlink[ibeats.back()]);
c@278:     }
c@277:   
c@278:     // REVERSE SEQUENCE OF IBEATS AND STORE AS BEATS
c@278:     for (uint i=0; i<ibeats.size(); i++)
c@278:     { 
c@278:         beats.push_back( static_cast<double>(ibeats[ibeats.size()-i-1]) );
c@278:     }
c@277: }
c@277: 
c@277: