comparison dsp/tempotracking/TempoTrackV2.cpp @ 52:4d1f32efcafd

* Add Matthew's newer beat tracking implementation

+/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
+
+/*
+    QM DSP Library
+
+    Centre for Digital Music, Queen Mary, University of London.
+    This file copyright 2008-2009 Matthew Davies and QMUL.
+    All rights reserved.
+*/
+
+#include "TempoTrackV2.h"
+
+#include <cmath>
+#include <cstdlib>
+
+
+//#define		FRAMESIZE	512
+//#define		BIGFRAMESIZE	1024
+#define   TWOPI 6.283185307179586232
+#define   EPS 0.0000008 // just some arbitrary small number
+
+TempoTrackV2::TempoTrackV2() { }
+TempoTrackV2::~TempoTrackV2() { }
+
+void
+TempoTrackV2::adapt_thresh(d_vec_t &df)
+{
+
+  d_vec_t smoothed(df.size());
+	
+	int p_post = 7;
+	int p_pre = 8;
+
+	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
+
+	// find threshold for first 't' samples, where a full average cannot be computed yet 
+	for (int i = 0;i <= t;i++)
+	{	
+            int k = std::min((i+p_pre),static_cast<int>(df.size()));
+		smoothed[i] = mean_array(df,1,k);
+	}
+	// find threshold for bulk of samples across a moving average from [i-p_pre,i+p_post]
+	for (uint i = t+1;i < df.size()-p_post;i++)
+	{
+		smoothed[i] = mean_array(df,i-p_pre,i+p_post);
+	}
+	// for last few samples calculate threshold, again, not enough samples to do as above
+	for (uint i = df.size()-p_post;i < df.size();i++)
+	{
+            int k = std::max((static_cast<int> (i) -p_post),1);
+		smoothed[i] = mean_array(df,k,df.size());
+	}
+
+	// subtract the threshold from the detection function and check that it is not less than 0
+	for (uint i = 0;i < df.size();i++)
+	{
+		df[i] -= smoothed[i];
+		if (df[i] < 0)
+		{
+			df[i] = 0;
+		}
+	}
+}
+
+double
+TempoTrackV2::mean_array(const d_vec_t &dfin,int start,int end)
+{
+
+	double sum = 0.;
+	
+	// find sum
+	for (int i = start;i < end+1;i++)
+	{
+		sum += dfin[i];
+	}
+
+	return static_cast<double> (sum / (end - start + 1) );	// average and return
+}
+
+void
+TempoTrackV2::filter_df(d_vec_t &df)
+{
+
+
+  d_vec_t a(3);
+  d_vec_t b(3);
+  d_vec_t	lp_df(df.size());
+
+  //equivalent in matlab to [b,a] = butter(2,0.4);
+	a[0] = 1.0000;
+	a[1] = -0.3695;
+	a[2] = 0.1958;
+	b[0] = 0.2066;
+	b[1] = 0.4131;
+	b[2] = 0.2066;
+	
+  double inp1 = 0.;
+  double inp2 = 0.;
+  double out1 = 0.;
+  double out2 = 0.;
+
+
+  // forwards filtering
+	for (uint i = 0;i < df.size();i++)
+	{
+    lp_df[i] =  b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
+    inp2 = inp1;
+    inp1 = df[i];
+    out2 = out1;
+    out1 = lp_df[i];
+	}
+
+
+  // copy forwards filtering to df...
+  // but, time-reversed, ready for backwards filtering
+	for (uint i = 0;i < df.size();i++)
+	{
+    df[i] = lp_df[df.size()-i];    
+  }
+
+	for (uint i = 0;i < df.size();i++)
+	{
+    lp_df[i] = 0.;    
+  }
+
+  inp1 = 0.; inp2 = 0.;
+  out1 = 0.; out2 = 0.;
+
+  // backwards filetering on time-reversed df
+	for (uint i = 0;i < df.size();i++)
+	{
+    lp_df[i] =  b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
+    inp2 = inp1;
+    inp1 = df[i];
+    out2 = out1;
+    out1 = lp_df[i];
+	}
+
+  // write the re-reversed (i.e. forward) version back to df
+	for (uint i = 0;i < df.size();i++)
+	{
+    df[i] = lp_df[df.size()-i];    
+  }
+
+
+}
+
+
+void
+TempoTrackV2::calculateBeatPeriod(const d_vec_t &df, d_vec_t &beat_period)
+{
+
+// to follow matlab.. split into 512 sample frames with a 128 hop size
+// calculate the acf,
+// then the rcf.. and then stick the rcfs as columns of a matrix
+// then call viterbi decoding with weight vector and transition matrix
+// and get best path
+
+  uint wv_len = 128;
+  double rayparam = 43.;
+
+  // make rayleigh weighting curve
+  d_vec_t wv(wv_len);
+  for (uint i=0; i<wv.size(); i++)
+  {
+    wv[i] = (static_cast<double> (i) / pow(rayparam,2.)) * exp((-1.*pow(-static_cast<double> (i),2.)) / (2.*pow(rayparam,2.)));
+  }
+
+
+  uint winlen = 512;
+  uint step = 128;
+
+  d_mat_t rcfmat;
+  int col_counter = -1;
+  // main loop for beat period calculation
+  for (uint i=0; i<(df.size()-winlen); i+=step)
+  {
+    // get dfframe
+    d_vec_t dfframe(winlen);
+    for (uint k=0; k<winlen; k++)
+    {
+      dfframe[k] = df[i+k];
+    }
+    // get rcf vector for current frame
+    d_vec_t rcf(wv_len);    
+    get_rcf(dfframe,wv,rcf);
+  
+    rcfmat.push_back( d_vec_t() ); // adds a new column
+    col_counter++;
+    for (uint j=0; j<rcf.size(); j++)
+    {
+      rcfmat[col_counter].push_back( rcf[j] );
+    }
+
+  }
+  
+  // now call viterbi decoding function
+  viterbi_decode(rcfmat,wv,beat_period);
+
+
+
+}
+
+
+void
+TempoTrackV2::get_rcf(const d_vec_t &dfframe_in, const d_vec_t &wv, d_vec_t &rcf)
+{
+  // calculate autocorrelation function
+  // then rcf
+  // just hard code for now... don't really need separate functions to do this
+
+  // make acf
+
+  d_vec_t dfframe(dfframe_in);
+
+  adapt_thresh(dfframe);
+
+  d_vec_t acf(dfframe.size());
+
+
+  for (uint lag=0; lag<dfframe.size(); lag++)
+  {
+
+    double sum = 0.;
+    double tmp = 0.;
+
+    for (uint n=0; n<(dfframe.size()-lag); n++)
+    {
+      tmp = dfframe[n] * dfframe[n+lag];    
+      sum += tmp;
+    }
+    acf[lag] = static_cast<double> (sum/ (dfframe.size()-lag));
+  }
+
+
+//  for (uint i=0; i<dfframe.size(); i++)
+//  {
+//    cout << dfframe[i] << " " << acf[i]  << endl;
+//  }
+
+//    cout << "~~~~~~~~~~~~~~" << endl;
+
+
+
+
+
+  // now apply comb filtering
+	int numelem = 4;
+	
+//	for (uint i = 1;i < 118;i++) // max beat period
+	for (uint i = 2;i < rcf.size();i++) // max beat period
+	{
+		for (int a = 1;a <= numelem;a++) // number of comb elements
+		{
+			for (int b = 1-a;b <= a-1;b++) // general state using normalisation of comb elements
+			{
+				rcf[i-1] += ( acf[(a*i+b)-1]*wv[i-1] ) / (2.*a-1.);	// calculate value for comb filter row
+			}
+		}
+	}
+  
+  // apply adaptive threshold to rcf
+  adapt_thresh(rcf);
+  
+  double rcfsum =0.;
+  for (uint i=0; i<rcf.size(); i++)
+  {
+ //  rcf[i] *= acf[i];
+    rcf[i] += EPS ;
+    rcfsum += rcf[i];
+  }
+
+  // normalise rcf to sum to unity
+  for (uint i=0; i<rcf.size(); i++)
+  {
+    rcf[i] /= (rcfsum + EPS);
+  }
+
+
+
+}
+
+void
+TempoTrackV2::viterbi_decode(const d_mat_t &rcfmat, const d_vec_t &wv, d_vec_t &beat_period)
+{
+
+  // make transition matrix
+	d_mat_t tmat;
+	for (uint i=0;i<wv.size();i++)
+	{
+		tmat.push_back ( d_vec_t() ); // adds a new column
+		for (uint j=0; j<wv.size(); j++)
+		{	
+			tmat[i].push_back(0.); // fill with zeros initially
+		}
+	}
+
+  double sigma = 8.;
+	for (uint i=20;i <wv.size()-20; i++)
+	{
+		for (uint j=20; j<wv.size()-20; j++)
+		{	
+      double mu = static_cast<double>(i);
+			tmat[i][j] = exp( (-1.*pow((j-mu),2.)) / (2.*pow(sigma,2.)) );
+		}
+	}
+
+  d_mat_t delta;
+  i_mat_t psi;
+	for (uint i=0;i <rcfmat.size(); i++)
+	{
+    delta.push_back( d_vec_t());
+    psi.push_back( i_vec_t());
+		for (uint j=0; j<rcfmat[i].size(); j++)
+		{	
+			delta[i].push_back(0.); // fill with zeros initially
+			psi[i].push_back(0); // fill with zeros initially
+		}
+	}
+
+
+  uint T = delta.size();
+  uint Q = delta[0].size();
+
+  // initialize first column of delta
+  for (uint j=0; j<Q; j++)
+  {
+    delta[0][j] = wv[j] * rcfmat[0][j];
+    psi[0][j] = 0;
+  }
+
+  double deltasum = 0.;
+  for (uint i=0; i<Q; i++)
+  {
+    deltasum += delta[0][i];
+  }      
+  for (uint i=0; i<Q; i++)
+  {
+    delta[0][i] /= (deltasum + EPS);
+  }      
+
+
+
+  for (uint t=1; t<T; t++)
+  {
+    d_vec_t tmp_vec(Q);
+
+    for (uint j=0; j<Q; j++)
+    {
+
+      for (uint i=0; i<Q; i++)
+      {
+        tmp_vec[i] = delta[t-1][i] * tmat[j][i];
+      }      
+   
+      delta[t][j] = get_max_val(tmp_vec);    
+
+      psi[t][j] = get_max_ind(tmp_vec);
+ 
+      delta[t][j] *= rcfmat[t][j];
+
+
+    }
+
+    double deltasum = 0.;
+    for (uint i=0; i<Q; i++)
+    {
+      deltasum += delta[t][i];
+    }      
+    for (uint i=0; i<Q; i++)
+    {
+      delta[t][i] /= (deltasum + EPS);
+    }      
+
+
+
+
+  }
+
+
+//  ofstream tmatfile;
+//  tmatfile.open("/home/matthewd/Desktop/tmat.txt");
+
+// 	for (uint i=0;i <delta.size(); i++)
+//	{
+//		for (uint j=0; j<delta[i].size(); j++)
+//		{	
+//      tmatfile << rcfmat[i][j] << endl;
+//		}
+//	}
+
+//  tmatfile.close();
+
+  i_vec_t bestpath(T);
+  d_vec_t tmp_vec(Q);
+  for (uint i=0; i<Q; i++)
+  {  
+    tmp_vec[i] = delta[T-1][i];
+  }
+
+  
+  bestpath[T-1] = get_max_ind(tmp_vec);
+ 
+  for (uint t=T-2; t>0 ;t--)
+  {
+    bestpath[t] = psi[t+1][bestpath[t+1]];
+  }
+  // very weird hack!
+  bestpath[0] = psi[1][bestpath[1]];
+
+//  for (uint i=0; i<bestpath.size(); i++)
+//  {
+//    cout << bestpath[i] << endl;
+//  }
+
+
+  uint lastind = 0;
+  for (uint i=0; i<T; i++)
+  {  
+    uint step = 128;
+ //   cout << bestpath[i] << " " << i << endl;
+    for (uint j=0; j<step; j++)
+    {
+      lastind = i*step+j;
+      beat_period[lastind] = bestpath[i];
+      
+    }
+  }
+
+  //fill in the last values...
+  for (uint i=lastind; i<beat_period.size(); i++)
+  {
+    beat_period[i] = beat_period[lastind];
+  }
+ 
+
+
+}
+
+double
+TempoTrackV2::get_max_val(const d_vec_t &df)
+{
+  double maxval = 0.;
+  for (uint i=0; i<df.size(); i++)
+  {
+
+    if (maxval < df[i])
+    {
+      maxval = df[i];
+    }
+
+  }
+
+    
+  return maxval;
+
+}
+
+int
+TempoTrackV2::get_max_ind(const d_vec_t &df)
+{
+
+  double maxval = 0.;
+  int ind = 0;
+  for (uint i=0; i<df.size(); i++)
+  {
+    if (maxval < df[i])
+    {
+      maxval = df[i];
+      ind = i;
+    }
+
+  }
+  
+  return ind;
+
+}
+
+void
+TempoTrackV2::normalise_vec(d_vec_t &df)
+{
+  double sum = 0.;
+  for (uint i=0; i<df.size(); i++)
+  {
+    sum += df[i];
+  }
+
+  for (uint i=0; i<df.size(); i++)
+  {
+    df[i]/= (sum + EPS);
+  }
+
+
+}
+
+void
+TempoTrackV2::calculateBeats(const d_vec_t &df, const d_vec_t &beat_period,
+                             d_vec_t &beats)
+{
+
+  d_vec_t cumscore(df.size());
+  i_vec_t backlink(df.size());
+  d_vec_t localscore(df.size());
+
+  // WHEN I FIGURE OUT HOW, I'LL WANT TO DO SOME FILTERING ON THIS... 
+  for (uint i=0; i<df.size(); i++)
+  {
+    localscore[i] = df[i];
+    backlink[i] = -1;
+  }
+
+  double tightness = 4.;
+  double alpha = 0.9;
+
+  // main loop
+  for (uint i=3*beat_period[0]; i<localscore.size(); i++)
+  {
+    int prange_min = -2*beat_period[i];
+    int prange_max = round(-0.5*beat_period[i]);
+
+    d_vec_t txwt (prange_max - prange_min + 1);
+    d_vec_t scorecands (txwt.size());
+
+    for (uint j=0;j<txwt.size();j++)
+    {
+      double mu = static_cast<double> (beat_period[i]);
+      txwt[j] = exp( -0.5*pow(tightness * log((round(2*mu)-j)/mu),2));
+
+      scorecands[j] = txwt[j] * cumscore[i+prange_min+j];
+    }
+
+    double vv = get_max_val(scorecands);
+    int xx = get_max_ind(scorecands);
+
+    cumscore[i] = alpha*vv + (1.-alpha)*localscore[i];
+
+    backlink[i] = i+prange_min+xx;
+
+  }
+
+
+  d_vec_t tmp_vec;
+  for (uint i=cumscore.size() - beat_period[beat_period.size()-1] ; i<cumscore.size(); i++)
+  {
+    tmp_vec.push_back(cumscore[i]);
+  }  
+
+  int startpoint = get_max_ind(tmp_vec) + cumscore.size() - beat_period[beat_period.size()-1] ;
+
+  i_vec_t ibeats;
+  ibeats.push_back(startpoint);
+  while (backlink[ibeats.back()] > 3*beat_period[0])
+  {
+    ibeats.push_back(backlink[ibeats.back()]);
+  }
+  
+
+  for (uint i=0; i<ibeats.size(); i++)
+  { 
+
+    beats.push_back( static_cast<double>(ibeats[i]) );
+
+ //   cout << ibeats[i] << " "  << beats[i] <<endl;
+  }
+}
+
+