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::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);
}
}
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;
}
double
DownBeat::measureSpecDiff(d_vec_t oldspec, d_vec_t newspec)
{
// JENSEN-SHANNON DIVERGENCE BETWEEN SPECTRAL FRAMES
unsigned int SPECSIZE = 512; // ONLY LOOK AT FIRST 512 SAMPLES OF SPECTRUM.
if (SPECSIZE > oldspec.size()/4) {
SPECSIZE = oldspec.size()/4;
}
double SD = 0.;
double sd1 = 0.;
double sumnew = 0.;
double sumold = 0.;
for (unsigned int i = 0;i < SPECSIZE;i++)
{
newspec[i] +=EPS;
oldspec[i] +=EPS;
sumnew+=newspec[i];
sumold+=oldspec[i];
}
for (unsigned int i = 0;i < SPECSIZE;i++)
{
newspec[i] /= (sumnew);
oldspec[i] /= (sumold);
// IF ANY SPECTRAL VALUES ARE 0 (SHOULDN'T BE ANY!) SET THEM TO 1
if (newspec[i] == 0)
{
newspec[i] = 1.;
}
if (oldspec[i] == 0)
{
oldspec[i] = 1.;
}
// JENSEN-SHANNON CALCULATION
sd1 = 0.5*oldspec[i] + 0.5*newspec[i];
SD = SD + (-sd1*log(sd1)) + (0.5*(oldspec[i]*log(oldspec[i]))) + (0.5*(newspec[i]*log(newspec[i])));
}
return SD;
}
void
DownBeat::findDownBeats(const float *audio,
size_t audioLength,
const d_vec_t &beats,
i_vec_t &downbeats)
{
// FIND DOWNBEATS BY PARTITIONING THE INPUT AUDIO FILE INTO BEAT SEGMENTS
// WHERE THE AUDIO FRAMES ARE DOWNSAMPLED BY A FACTOR OF 16 (fs ~= 2700Hz)
// THEN TAKING THE JENSEN-SHANNON DIVERGENCE BETWEEN BEAT SYNCHRONOUS SPECTRAL FRAMES
// IMPLEMENTATION (MOSTLY) FOLLOWS:
// DAVIES AND PLUMBLEY "A SPECTRAL DIFFERENCE APPROACH TO EXTRACTING DOWNBEATS IN MUSICAL AUDIO"
// EUSIPCO 2006, FLORENCE, ITALY
d_vec_t newspec(m_beatframesize / 2); // magnitude spectrum of current beat
d_vec_t oldspec(m_beatframesize / 2); // magnitude spectrum of previous beat
m_beatsd.clear();
if (audioLength == 0) return;
for (size_t i = 0; i + 1 < beats.size(); ++i) {
// Copy the extents of the current beat from downsampled array
// into beat frame buffer
size_t beatstart = (beats[i] * m_increment) / m_factor;
size_t beatend = (beats[i+1] * m_increment) / m_factor;
if (beatend >= audioLength) beatend = audioLength - 1;
if (beatend < beatstart) beatend = beatstart;
size_t beatlen = beatend - beatstart;
// Also apply a Hanning window to the beat frame buffer, sized
// to the beat extents rather than the frame size. (Because
// the size varies, it's easier to do this by hand than use
// our Window abstraction.)
// std::cerr << "beatlen = " << beatlen << std::endl;
// float rms = 0;
for (size_t j = 0; j < beatlen && j < m_beatframesize; ++j) {
double mul = 0.5 * (1.0 - cos(TWO_PI * (double(j) / double(beatlen))));
m_beatframe[j] = audio[beatstart + j] * mul;
// rms += m_beatframe[j] * m_beatframe[j];
}
// rms = sqrt(rms);
// std::cerr << "beat " << i << ": audio rms " << rms << std::endl;
for (size_t j = beatlen; j < m_beatframesize; ++j) {
m_beatframe[j] = 0.0;
}
// Now FFT beat frame
m_fft->process(false, m_beatframe, m_fftRealOut, m_fftImagOut);
// Calculate magnitudes
for (size_t j = 0; j < m_beatframesize/2; ++j) {
newspec[j] = sqrt(m_fftRealOut[j] * m_fftRealOut[j] +
m_fftImagOut[j] * m_fftImagOut[j]);
}
// Preserve peaks by applying adaptive threshold
MathUtilities::adaptiveThreshold(newspec);
// Calculate JS divergence between new and old spectral frames
if (i > 0) { // otherwise we have no previous frame
m_beatsd.push_back(measureSpecDiff(oldspec, newspec));
// std::cerr << "specdiff: " << m_beatsd[m_beatsd.size()-1] << std::endl;
}
// Copy newspec across to old
for (size_t j = 0; j < m_beatframesize/2; ++j) {
oldspec[j] = newspec[j];
}
}
// We now have all spectral difference measures in specdiff
int timesig = m_bpb;
if (timesig == 0) timesig = 4;
d_vec_t dbcand(timesig); // downbeat candidates
for (int beat = 0; beat < timesig; ++beat) {
dbcand[beat] = 0;
}
// look for beat transition which leads to greatest spectral change
for (int beat = 0; beat < timesig; ++beat) {
int count = 0;
for (int example = beat-1; example < (int)m_beatsd.size(); example += timesig) {
if (example < 0) continue;
dbcand[beat] += (m_beatsd[example]) / timesig;
++count;
}
if (count > 0) dbcand[beat] /= count;
// std::cerr << "dbcand[" << beat << "] = " << dbcand[beat] << std::endl;
}
// first downbeat is beat at index of maximum value of dbcand
int dbind = MathUtilities::getMax(dbcand);
// remaining downbeats are at timesig intervals from the first
for (int i = dbind; i < (int)beats.size(); i += timesig) {
downbeats.push_back(i);
}
}
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::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]);
}
}