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livetrax/libs/qm-dsp/dsp/tempotracking/TempoTrackV2.cpp

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/* -*- 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.
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. See the file
COPYING included with this distribution for more information.
*/
#include "TempoTrackV2.h"
#include <cmath>
#include <cstdlib>
#include <iostream>
#include "maths/MathUtilities.h"
#define EPS 0.0000008 // just some arbitrary small number
TempoTrackV2::TempoTrackV2(float rate, size_t increment) :
m_rate(rate), m_increment(increment) { }
TempoTrackV2::~TempoTrackV2() { }
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 (unsigned int 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 (unsigned int i = 0;i < df.size();i++)
{
df[i] = lp_df[df.size()-i-1];
}
for (unsigned int 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 (unsigned int 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 (unsigned int i = 0;i < df.size();i++)
{
df[i] = lp_df[df.size()-i-1];
}
}
void
TempoTrackV2::calculateBeatPeriod(const vector<double> &df,
vector<double> &beat_period,
vector<double> &tempi)
{
// 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
unsigned int wv_len = 128;
double rayparam = 43.;
// make rayleigh weighting curve
d_vec_t wv(wv_len);
for (unsigned int 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.)));
}
// beat tracking frame size (roughly 6 seconds) and hop (1.5 seconds)
unsigned int winlen = 512;
unsigned int step = 128;
// matrix to store output of comb filter bank, increment column of matrix at each frame
d_mat_t rcfmat;
int col_counter = -1;
// main loop for beat period calculation
for (unsigned int i=0; i+winlen<df.size(); i+=step)
{
// get dfframe
d_vec_t dfframe(winlen);
for (unsigned int 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 (unsigned int j=0; j<rcf.size(); j++)
{
rcfmat[col_counter].push_back( rcf[j] );
}
}
// now call viterbi decoding function
viterbi_decode(rcfmat,wv,beat_period,tempi);
}
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);
MathUtilities::adaptiveThreshold(dfframe);
d_vec_t acf(dfframe.size());
for (unsigned int lag=0; lag<dfframe.size(); lag++)
{
double sum = 0.;
double tmp = 0.;
for (unsigned int n=0; n<(dfframe.size()-lag); n++)
{
tmp = dfframe[n] * dfframe[n+lag];
sum += tmp;
}
acf[lag] = static_cast<double> (sum/ (dfframe.size()-lag));
}
// now apply comb filtering
int numelem = 4;
for (unsigned int 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
MathUtilities::adaptiveThreshold(rcf);
double rcfsum =0.;
for (unsigned int i=0; i<rcf.size(); i++)
{
rcf[i] += EPS ;
rcfsum += rcf[i];
}
// normalise rcf to sum to unity
for (unsigned int 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, d_vec_t &tempi)
{
// following Kevin Murphy's Viterbi decoding to get best path of
// beat periods through rfcmat
// make transition matrix
d_mat_t tmat;
for (unsigned int i=0;i<wv.size();i++)
{
tmat.push_back ( d_vec_t() ); // adds a new column
for (unsigned int j=0; j<wv.size(); j++)
{
tmat[i].push_back(0.); // fill with zeros initially
}
}
// variance of Gaussians in transition matrix
// formed of Gaussians on diagonal - implies slow tempo change
double sigma = 8.;
// don't want really short beat periods, or really long ones
for (unsigned int i=20;i <wv.size()-20; i++)
{
for (unsigned int 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.)) );
}
}
// parameters for Viterbi decoding... this part is taken from
// Murphy's matlab
d_mat_t delta;
i_mat_t psi;
for (unsigned int i=0;i <rcfmat.size(); i++)
{
delta.push_back( d_vec_t());
psi.push_back( i_vec_t());
for (unsigned int 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
}
}
unsigned int T = delta.size();
if (T < 2) return; // can't do anything at all meaningful
unsigned int Q = delta[0].size();
// initialize first column of delta
for (unsigned int j=0; j<Q; j++)
{
delta[0][j] = wv[j] * rcfmat[0][j];
psi[0][j] = 0;
}
double deltasum = 0.;
for (unsigned int i=0; i<Q; i++)
{
deltasum += delta[0][i];
}
for (unsigned int i=0; i<Q; i++)
{
delta[0][i] /= (deltasum + EPS);
}
for (unsigned int t=1; t<T; t++)
{
d_vec_t tmp_vec(Q);
for (unsigned int j=0; j<Q; j++)
{
for (unsigned int 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];
}
// normalise current delta column
double deltasum = 0.;
for (unsigned int i=0; i<Q; i++)
{
deltasum += delta[t][i];
}
for (unsigned int i=0; i<Q; i++)
{
delta[t][i] /= (deltasum + EPS);
}
}
i_vec_t bestpath(T);
d_vec_t tmp_vec(Q);
for (unsigned int i=0; i<Q; i++)
{
tmp_vec[i] = delta[T-1][i];
}
// find starting point - best beat period for "last" frame
bestpath[T-1] = get_max_ind(tmp_vec);
// backtrace through index of maximum values in psi
for (unsigned int t=T-2; t>0 ;t--)
{
bestpath[t] = psi[t+1][bestpath[t+1]];
}
// weird but necessary hack -- couldn't get above loop to terminate at t >= 0
bestpath[0] = psi[1][bestpath[1]];
unsigned int lastind = 0;
for (unsigned int i=0; i<T; i++)
{
unsigned int step = 128;
for (unsigned int j=0; j<step; j++)
{
lastind = i*step+j;
beat_period[lastind] = bestpath[i];
}
// std::cerr << "bestpath[" << i << "] = " << bestpath[i] << " (used for beat_periods " << i*step << " to " << i*step+step-1 << ")" << std::endl;
}
//fill in the last values...
for (unsigned int i=lastind; i<beat_period.size(); i++)
{
beat_period[i] = beat_period[lastind];
}
for (unsigned int i = 0; i < beat_period.size(); i++)
{
tempi.push_back((60. * m_rate / m_increment)/beat_period[i]);
}
}
double
TempoTrackV2::get_max_val(const d_vec_t &df)
{
double maxval = 0.;
for (unsigned int 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 (unsigned int 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 (unsigned int i=0; i<df.size(); i++)
{
sum += df[i];
}
for (unsigned int i=0; i<df.size(); i++)
{
df[i]/= (sum + EPS);
}
}
void
TempoTrackV2::calculateBeats(const vector<double> &df,
const vector<double> &beat_period,
vector<double> &beats)
{
if (df.empty() || beat_period.empty()) return;
d_vec_t cumscore(df.size()); // store cumulative score
i_vec_t backlink(df.size()); // backlink (stores best beat locations at each time instant)
d_vec_t localscore(df.size()); // localscore, for now this is the same as the detection function
for (unsigned int i=0; i<df.size(); i++)
{
localscore[i] = df[i];
backlink[i] = -1;
}
double tightness = 4.;
double alpha = 0.9;
// main loop
for (unsigned int i=0; i<localscore.size(); i++)
{
int prange_min = -2*beat_period[i];
int prange_max = round(-0.5*beat_period[i]);
// transition range
d_vec_t txwt (prange_max - prange_min + 1);
d_vec_t scorecands (txwt.size());
for (unsigned int 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));
// IF IN THE ALLOWED RANGE, THEN LOOK AT CUMSCORE[I+PRANGE_MIN+J
// ELSE LEAVE AT DEFAULT VALUE FROM INITIALISATION: D_VEC_T SCORECANDS (TXWT.SIZE());
int cscore_ind = i+prange_min+j;
if (cscore_ind >= 0)
{
scorecands[j] = txwt[j] * cumscore[cscore_ind];
}
}
// find max value and index of maximum value
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;
// std::cerr << "backlink[" << i << "] <= " << backlink[i] << std::endl;
}
// STARTING POINT, I.E. LAST BEAT.. PICK A STRONG POINT IN cumscore VECTOR
d_vec_t tmp_vec;
for (unsigned int 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] ;
// can happen if no results obtained earlier (e.g. input too short)
if (startpoint >= backlink.size()) startpoint = backlink.size()-1;
// USE BACKLINK TO GET EACH NEW BEAT (TOWARDS THE BEGINNING OF THE FILE)
// BACKTRACKING FROM THE END TO THE BEGINNING.. MAKING SURE NOT TO GO BEFORE SAMPLE 0
i_vec_t ibeats;
ibeats.push_back(startpoint);
// std::cerr << "startpoint = " << startpoint << std::endl;
while (backlink[ibeats.back()] > 0)
{
// std::cerr << "backlink[" << ibeats.back() << "] = " << backlink[ibeats.back()] << std::endl;
int b = ibeats.back();
if (backlink[b] == b) break; // shouldn't happen... haha
ibeats.push_back(backlink[b]);
}
// REVERSE SEQUENCE OF IBEATS AND STORE AS BEATS
for (unsigned int i=0; i<ibeats.size(); i++)
{
beats.push_back( static_cast<double>(ibeats[ibeats.size()-i-1]) );
}
}