1 /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
6 Centre for Digital Music, Queen Mary, University of London.
7 This file copyright 2008-2009 Matthew Davies and QMUL.
9 This program is free software; you can redistribute it and/or
10 modify it under the terms of the GNU General Public License as
11 published by the Free Software Foundation; either version 2 of the
12 License, or (at your option) any later version. See the file
13 COPYING included with this distribution for more information.
16 #include "TempoTrackV2.h"
22 #include "maths/MathUtilities.h"
24 #define EPS 0.0000008 // just some arbitrary small number
26 TempoTrackV2::TempoTrackV2(float rate, size_t increment) :
27 m_rate(rate), m_increment(increment) { }
28 TempoTrackV2::~TempoTrackV2() { }
31 TempoTrackV2::filter_df(d_vec_t &df)
35 d_vec_t lp_df(df.size());
37 //equivalent in matlab to [b,a] = butter(2,0.4);
52 for (unsigned int i = 0;i < df.size();i++)
54 lp_df[i] = b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
61 // copy forwards filtering to df...
62 // but, time-reversed, ready for backwards filtering
63 for (unsigned int i = 0;i < df.size();i++)
65 df[i] = lp_df[df.size()-i-1];
68 for (unsigned int i = 0;i < df.size();i++)
76 // backwards filetering on time-reversed df
77 for (unsigned int i = 0;i < df.size();i++)
79 lp_df[i] = b[0]*df[i] + b[1]*inp1 + b[2]*inp2 - a[1]*out1 - a[2]*out2;
86 // write the re-reversed (i.e. forward) version back to df
87 for (unsigned int i = 0;i < df.size();i++)
89 df[i] = lp_df[df.size()-i-1];
95 // This function now allows for a user to specify an inputtempo (in BPM)
96 // and a flag "constraintempo" which replaces the general rayleigh weighting for periodicities
97 // with a gaussian which is centered around the input tempo
98 // Note, if inputtempo = 120 and constraintempo = false, then functionality is
101 TempoTrackV2::calculateBeatPeriod(const vector<double> &df,
102 vector<double> &beat_period,
103 vector<double> &tempi,
104 double inputtempo, bool constraintempo)
106 // to follow matlab.. split into 512 sample frames with a 128 hop size
107 // calculate the acf,
108 // then the rcf.. and then stick the rcfs as columns of a matrix
109 // then call viterbi decoding with weight vector and transition matrix
112 unsigned int wv_len = 128;
115 // the default value of inputtempo in the beat tracking plugin is 120
116 // so if the user specifies a different inputtempo, the rayparam will be updated
118 // note: 60*44100/512 is a magic number
119 // this might (will?) break if a user specifies a different frame rate for the onset detection function
120 double rayparam = (60*44100/512)/inputtempo;
122 // these debug statements can be removed.
123 // std::cerr << "inputtempo" << inputtempo << std::endl;
124 // std::cerr << "rayparam" << rayparam << std::endl;
125 // std::cerr << "constraintempo" << constraintempo << std::endl;
127 // make rayleigh weighting curve
130 // check whether or not to use rayleigh weighting (if constraintempo is false)
131 // or use gaussian weighting it (constraintempo is true)
134 for (unsigned int i=0; i<wv.size(); i++)
137 // do a gaussian weighting instead of rayleigh
138 wv[i] = exp( (-1.*pow((static_cast<double> (i)-rayparam),2.)) / (2.*pow(rayparam/4.,2.)) );
143 for (unsigned int i=0; i<wv.size(); i++)
146 // standard rayleigh weighting over periodicities
147 wv[i] = (static_cast<double> (i) / pow(rayparam,2.)) * exp((-1.*pow(-static_cast<double> (i),2.)) / (2.*pow(rayparam,2.)));
151 // beat tracking frame size (roughly 6 seconds) and hop (1.5 seconds)
152 unsigned int winlen = 512;
153 unsigned int step = 128;
155 // matrix to store output of comb filter bank, increment column of matrix at each frame
157 int col_counter = -1;
159 // main loop for beat period calculation
160 for (unsigned int i=0; i+winlen<df.size(); i+=step)
163 d_vec_t dfframe(winlen);
164 for (unsigned int k=0; k<winlen; k++)
166 dfframe[k] = df[i+k];
168 // get rcf vector for current frame
170 get_rcf(dfframe,wv,rcf);
172 rcfmat.push_back( d_vec_t() ); // adds a new column
174 for (unsigned int j=0; j<rcf.size(); j++)
176 rcfmat[col_counter].push_back( rcf[j] );
180 // now call viterbi decoding function
181 viterbi_decode(rcfmat,wv,beat_period,tempi);
186 TempoTrackV2::get_rcf(const d_vec_t &dfframe_in, const d_vec_t &wv, d_vec_t &rcf)
188 // calculate autocorrelation function
190 // just hard code for now... don't really need separate functions to do this
194 d_vec_t dfframe(dfframe_in);
196 MathUtilities::adaptiveThreshold(dfframe);
198 d_vec_t acf(dfframe.size());
201 for (unsigned int lag=0; lag<dfframe.size(); lag++)
206 for (unsigned int n=0; n<(dfframe.size()-lag); n++)
208 tmp = dfframe[n] * dfframe[n+lag];
211 acf[lag] = static_cast<double> (sum/ (dfframe.size()-lag));
214 // now apply comb filtering
217 for (unsigned int i = 2;i < rcf.size();i++) // max beat period
219 for (int a = 1;a <= numelem;a++) // number of comb elements
221 for (int b = 1-a;b <= a-1;b++) // general state using normalisation of comb elements
223 rcf[i-1] += ( acf[(a*i+b)-1]*wv[i-1] ) / (2.*a-1.); // calculate value for comb filter row
228 // apply adaptive threshold to rcf
229 MathUtilities::adaptiveThreshold(rcf);
232 for (unsigned int i=0; i<rcf.size(); i++)
238 // normalise rcf to sum to unity
239 for (unsigned int i=0; i<rcf.size(); i++)
241 rcf[i] /= (rcfsum + EPS);
246 TempoTrackV2::viterbi_decode(const d_mat_t &rcfmat, const d_vec_t &wv, d_vec_t &beat_period, d_vec_t &tempi)
248 // following Kevin Murphy's Viterbi decoding to get best path of
249 // beat periods through rfcmat
251 // make transition matrix
253 for (unsigned int i=0;i<wv.size();i++)
255 tmat.push_back ( d_vec_t() ); // adds a new column
256 for (unsigned int j=0; j<wv.size(); j++)
258 tmat[i].push_back(0.); // fill with zeros initially
262 // variance of Gaussians in transition matrix
263 // formed of Gaussians on diagonal - implies slow tempo change
265 // don't want really short beat periods, or really long ones
266 for (unsigned int i=20;i <wv.size()-20; i++)
268 for (unsigned int j=20; j<wv.size()-20; j++)
270 double mu = static_cast<double>(i);
271 tmat[i][j] = exp( (-1.*pow((j-mu),2.)) / (2.*pow(sigma,2.)) );
275 // parameters for Viterbi decoding... this part is taken from
280 for (unsigned int i=0;i <rcfmat.size(); i++)
282 delta.push_back( d_vec_t());
283 psi.push_back( i_vec_t());
284 for (unsigned int j=0; j<rcfmat[i].size(); j++)
286 delta[i].push_back(0.); // fill with zeros initially
287 psi[i].push_back(0); // fill with zeros initially
292 unsigned int T = delta.size();
294 if (T < 2) return; // can't do anything at all meaningful
296 unsigned int Q = delta[0].size();
298 // initialize first column of delta
299 for (unsigned int j=0; j<Q; j++)
301 delta[0][j] = wv[j] * rcfmat[0][j];
305 double deltasum = 0.;
306 for (unsigned int i=0; i<Q; i++)
308 deltasum += delta[0][i];
310 for (unsigned int i=0; i<Q; i++)
312 delta[0][i] /= (deltasum + EPS);
316 for (unsigned int t=1; t<T; t++)
320 for (unsigned int j=0; j<Q; j++)
322 for (unsigned int i=0; i<Q; i++)
324 tmp_vec[i] = delta[t-1][i] * tmat[j][i];
327 delta[t][j] = get_max_val(tmp_vec);
329 psi[t][j] = get_max_ind(tmp_vec);
331 delta[t][j] *= rcfmat[t][j];
334 // normalise current delta column
335 double deltasum = 0.;
336 for (unsigned int i=0; i<Q; i++)
338 deltasum += delta[t][i];
340 for (unsigned int i=0; i<Q; i++)
342 delta[t][i] /= (deltasum + EPS);
348 for (unsigned int i=0; i<Q; i++)
350 tmp_vec[i] = delta[T-1][i];
353 // find starting point - best beat period for "last" frame
354 bestpath[T-1] = get_max_ind(tmp_vec);
356 // backtrace through index of maximum values in psi
357 for (unsigned int t=T-2; t>0 ;t--)
359 bestpath[t] = psi[t+1][bestpath[t+1]];
362 // weird but necessary hack -- couldn't get above loop to terminate at t >= 0
363 bestpath[0] = psi[1][bestpath[1]];
365 unsigned int lastind = 0;
366 for (unsigned int i=0; i<T; i++)
368 unsigned int step = 128;
369 for (unsigned int j=0; j<step; j++)
372 beat_period[lastind] = bestpath[i];
374 // std::cerr << "bestpath[" << i << "] = " << bestpath[i] << " (used for beat_periods " << i*step << " to " << i*step+step-1 << ")" << std::endl;
377 //fill in the last values...
378 for (unsigned int i=lastind; i<beat_period.size(); i++)
380 beat_period[i] = beat_period[lastind];
383 for (unsigned int i = 0; i < beat_period.size(); i++)
385 tempi.push_back((60. * m_rate / m_increment)/beat_period[i]);
390 TempoTrackV2::get_max_val(const d_vec_t &df)
393 for (unsigned int i=0; i<df.size(); i++)
405 TempoTrackV2::get_max_ind(const d_vec_t &df)
409 for (unsigned int i=0; i<df.size(); i++)
422 TempoTrackV2::normalise_vec(d_vec_t &df)
425 for (unsigned int i=0; i<df.size(); i++)
430 for (unsigned int i=0; i<df.size(); i++)
437 // this function has been updated to allow the "alpha" and "tightness" parameters
438 // of the dynamic program to be set by the user
439 // the default value of alpha = 0.9 and tightness = 4
441 TempoTrackV2::calculateBeats(const vector<double> &df,
442 const vector<double> &beat_period,
443 vector<double> &beats, double alpha, double tightness)
445 if (df.empty() || beat_period.empty()) return;
447 d_vec_t cumscore(df.size()); // store cumulative score
448 i_vec_t backlink(df.size()); // backlink (stores best beat locations at each time instant)
449 d_vec_t localscore(df.size()); // localscore, for now this is the same as the detection function
451 for (unsigned int i=0; i<df.size(); i++)
453 localscore[i] = df[i];
457 //double tightness = 4.;
458 //double alpha = 0.9;
460 // debug statements that can be removed.
461 // std::cerr << "alpha" << alpha << std::endl;
462 // std::cerr << "tightness" << tightness << std::endl;
465 for (unsigned int i=0; i<localscore.size(); i++)
467 int prange_min = -2*beat_period[i];
468 int prange_max = round(-0.5*beat_period[i]);
471 d_vec_t txwt (prange_max - prange_min + 1);
472 d_vec_t scorecands (txwt.size());
474 for (unsigned int j=0;j<txwt.size();j++)
476 double mu = static_cast<double> (beat_period[i]);
477 txwt[j] = exp( -0.5*pow(tightness * log((round(2*mu)-j)/mu),2));
479 // IF IN THE ALLOWED RANGE, THEN LOOK AT CUMSCORE[I+PRANGE_MIN+J
480 // ELSE LEAVE AT DEFAULT VALUE FROM INITIALISATION: D_VEC_T SCORECANDS (TXWT.SIZE());
482 int cscore_ind = i+prange_min+j;
485 scorecands[j] = txwt[j] * cumscore[cscore_ind];
489 // find max value and index of maximum value
490 double vv = get_max_val(scorecands);
491 int xx = get_max_ind(scorecands);
493 cumscore[i] = alpha*vv + (1.-alpha)*localscore[i];
494 backlink[i] = i+prange_min+xx;
496 // std::cerr << "backlink[" << i << "] <= " << backlink[i] << std::endl;
499 // STARTING POINT, I.E. LAST BEAT.. PICK A STRONG POINT IN cumscore VECTOR
501 for (unsigned int i=cumscore.size() - beat_period[beat_period.size()-1] ; i<cumscore.size(); i++)
503 tmp_vec.push_back(cumscore[i]);
506 int startpoint = get_max_ind(tmp_vec) + cumscore.size() - beat_period[beat_period.size()-1] ;
508 // can happen if no results obtained earlier (e.g. input too short)
509 if (startpoint >= (int)backlink.size()) startpoint = backlink.size()-1;
511 // USE BACKLINK TO GET EACH NEW BEAT (TOWARDS THE BEGINNING OF THE FILE)
512 // BACKTRACKING FROM THE END TO THE BEGINNING.. MAKING SURE NOT TO GO BEFORE SAMPLE 0
514 ibeats.push_back(startpoint);
515 // std::cerr << "startpoint = " << startpoint << std::endl;
516 while (backlink[ibeats.back()] > 0)
518 // std::cerr << "backlink[" << ibeats.back() << "] = " << backlink[ibeats.back()] << std::endl;
519 int b = ibeats.back();
520 if (backlink[b] == b) break; // shouldn't happen... haha
521 ibeats.push_back(backlink[b]);
524 // REVERSE SEQUENCE OF IBEATS AND STORE AS BEATS
525 for (unsigned int i=0; i<ibeats.size(); i++)
527 beats.push_back( static_cast<double>(ibeats[ibeats.size()-i-1]) );