Cepstral Pitch Tracker

/* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */

/*

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    The above copyright notice and this permission notice shall be

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    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,

    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF

    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND

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*/

#include "CepstrumPitchTracker.h"

#include "vamp-sdk/FFT.h"

#include <vector>

#include <algorithm>

#include <cstdio>

#include <cmath>

#include <complex>

using std::string;

using std::vector;

using Vamp::RealTime;

CepstrumPitchTracker::Hypothesis::Hypothesis()

{

    m_state = New;

}

CepstrumPitchTracker::Hypothesis::~Hypothesis()

{

}

bool

CepstrumPitchTracker::Hypothesis::isWithinTolerance(Estimate s) const

{

    if (m_pending.empty()) {

        return true;

    }

    // check we are within a relatively close tolerance of the last

    // candidate

    Estimate last = m_pending[m_pending.size()-1];

    double r = s.freq / last.freq;

    int cents = lrint(1200.0 * (log(r) / log(2.0)));

    if (cents < -60 || cents > 60) return false;

    // and within a slightly bigger tolerance of the current mean

    double meanFreq = getMeanFrequency();

    r = s.freq / meanFreq;

    cents = lrint(1200.0 * (log(r) / log(2.0)));

    if (cents < -80 || cents > 80) return false;

    return true;

}

bool

CepstrumPitchTracker::Hypothesis::isOutOfDateFor(Estimate s) const

{

    if (m_pending.empty()) return false;

    return ((s.time - m_pending[m_pending.size()-1].time) > 

            RealTime::fromMilliseconds(40));

}

bool 

CepstrumPitchTracker::Hypothesis::isSatisfied() const

{

    if (m_pending.empty()) return false;

    double meanConfidence = 0.0;

    for (int i = 0; i < m_pending.size(); ++i) {

        meanConfidence += m_pending[i].confidence;

    }

    meanConfidence /= m_pending.size();

    int lengthRequired = 10000;

    if (meanConfidence > 0.0) {

        lengthRequired = int(2.0 / meanConfidence + 0.5);

    }

    return (m_pending.size() > lengthRequired);

}

bool

CepstrumPitchTracker::Hypothesis::accept(Estimate s)

{

    bool accept = false;

    switch (m_state) {

    case New:

        m_state = Provisional;

        accept = true;

        break;

    case Provisional:

        if (isOutOfDateFor(s)) {

            m_state = Rejected;

        } else if (isWithinTolerance(s)) {

            accept = true;

        }

        break;

    case Satisfied:

        if (isOutOfDateFor(s)) {

            m_state = Expired;

        } else if (isWithinTolerance(s)) {

            accept = true;

        }

        break;

    case Rejected:

        break;

    case Expired:

        break;

    }

    if (accept) {

        m_pending.push_back(s);

        if (m_state == Provisional && isSatisfied()) {

            m_state = Satisfied;

        }

    }

    return accept;

}        

CepstrumPitchTracker::Hypothesis::State

CepstrumPitchTracker::Hypothesis::getState() const

{

    return m_state;

}

CepstrumPitchTracker::Hypothesis::Estimates

CepstrumPitchTracker::Hypothesis::getAcceptedEstimates() const

{

    if (m_state == Satisfied || m_state == Expired) {

        return m_pending;

    } else {

        return Estimates();

    }

}

double

CepstrumPitchTracker::Hypothesis::getMeanFrequency() const

{

    double acc = 0.0;

    for (int i = 0; i < m_pending.size(); ++i) {

        acc += m_pending[i].freq;

    }

    acc /= m_pending.size();

    return acc;

}

CepstrumPitchTracker::Hypothesis::Note

CepstrumPitchTracker::Hypothesis::getAveragedNote() const

{

    Note n;

    if (!(m_state == Satisfied || m_state == Expired)) {

        n.freq = 0.0;

        n.time = RealTime::zeroTime;

        n.duration = RealTime::zeroTime;

        return n;

    }

    n.time = m_pending.begin()->time;

    Estimates::const_iterator i = m_pending.end();

    --i;

    n.duration = i->time - n.time;

    // just mean frequency for now, but this isn't at all right perceptually

    n.freq = getMeanFrequency();

    return n;

}

CepstrumPitchTracker::CepstrumPitchTracker(float inputSampleRate) :

    Plugin(inputSampleRate),

    m_channels(0),

    m_stepSize(256),

    m_blockSize(1024),

    m_fmin(50),

    m_fmax(900),

    m_vflen(1),

    m_binFrom(0),

    m_binTo(0),

    m_bins(0)

{

}

CepstrumPitchTracker::~CepstrumPitchTracker()

{

}

string

CepstrumPitchTracker::getIdentifier() const

{

    return "cepstrum-pitch";

}

string

CepstrumPitchTracker::getName() const

{

    return "Cepstrum Pitch Tracker";

}

string

CepstrumPitchTracker::getDescription() const

{

    return "Estimate f0 of monophonic material using a cepstrum method.";

}

string

CepstrumPitchTracker::getMaker() const

{

    return "Chris Cannam";

}

int

CepstrumPitchTracker::getPluginVersion() const

{

    // Increment this each time you release a version that behaves

    // differently from the previous one

    return 1;

}

string

CepstrumPitchTracker::getCopyright() const

{

    return "Freely redistributable (BSD license)";

}

CepstrumPitchTracker::InputDomain

CepstrumPitchTracker::getInputDomain() const

{

    return FrequencyDomain;

}

size_t

CepstrumPitchTracker::getPreferredBlockSize() const

{

    return 1024;

}

size_t 

CepstrumPitchTracker::getPreferredStepSize() const

{

    return 256;

}

size_t

CepstrumPitchTracker::getMinChannelCount() const

{

    return 1;

}

size_t

CepstrumPitchTracker::getMaxChannelCount() const

{

    return 1;

}

CepstrumPitchTracker::ParameterList

CepstrumPitchTracker::getParameterDescriptors() const

{

    ParameterList list;

    return list;

}

float

CepstrumPitchTracker::getParameter(string identifier) const

{

    return 0.f;

}

void

CepstrumPitchTracker::setParameter(string identifier, float value) 

{

}

CepstrumPitchTracker::ProgramList

CepstrumPitchTracker::getPrograms() const

{

    ProgramList list;

    return list;

}

string

CepstrumPitchTracker::getCurrentProgram() const

{

    return ""; // no programs

}

void

CepstrumPitchTracker::selectProgram(string name)

{

}

CepstrumPitchTracker::OutputList

CepstrumPitchTracker::getOutputDescriptors() const

{

    OutputList outputs;

    int n = 0;

    OutputDescriptor d;

    d.identifier = "f0";

    d.name = "Estimated f0";

    d.description = "Estimated fundamental frequency";

    d.unit = "Hz";

    d.hasFixedBinCount = true;

    d.binCount = 1;

    d.hasKnownExtents = true;

    d.minValue = m_fmin;

    d.maxValue = m_fmax;

    d.isQuantized = false;

    d.sampleType = OutputDescriptor::FixedSampleRate;

    d.sampleRate = (m_inputSampleRate / m_stepSize);

    d.hasDuration = false;

    outputs.push_back(d);

    d.identifier = "notes";

    d.name = "Notes";

    d.description = "Derived fixed-pitch note frequencies";

    d.unit = "Hz";

    d.hasFixedBinCount = true;

    d.binCount = 1;

    d.hasKnownExtents = true;

    d.minValue = m_fmin;

    d.maxValue = m_fmax;

    d.isQuantized = false;

    d.sampleType = OutputDescriptor::FixedSampleRate;

    d.sampleRate = (m_inputSampleRate / m_stepSize);

    d.hasDuration = true;

    outputs.push_back(d);

    return outputs;

}

bool

CepstrumPitchTracker::initialise(size_t channels, size_t stepSize, size_t blockSize)

{

    if (channels < getMinChannelCount() ||

        channels > getMaxChannelCount()) return false;

//    std::cerr << "CepstrumPitchTracker::initialise: channels = " << channels

//              << ", stepSize = " << stepSize << ", blockSize = " << blockSize

//              << std::endl;

    m_channels = channels;

    m_stepSize = stepSize;

    m_blockSize = blockSize;

    m_binFrom = int(m_inputSampleRate / m_fmax);

    m_binTo = int(m_inputSampleRate / m_fmin); 

    if (m_binTo >= (int)m_blockSize / 2) {

        m_binTo = m_blockSize / 2 - 1;

    }

    m_bins = (m_binTo - m_binFrom) + 1;

    reset();

    return true;

}

void

CepstrumPitchTracker::reset()

{

}

void

CepstrumPitchTracker::addFeaturesFrom(Hypothesis h, FeatureSet &fs)

{

    Hypothesis::Estimates es = h.getAcceptedEstimates();

    for (int i = 0; i < es.size(); ++i) {

        Feature f;

        f.hasTimestamp = true;

        f.timestamp = es[i].time;

        f.values.push_back(es[i].freq);

        fs[0].push_back(f);

    }

    Feature nf;

    nf.hasTimestamp = true;

    nf.hasDuration = true;

    Hypothesis::Note n = h.getAveragedNote();

    nf.timestamp = n.time;

    nf.duration = n.duration;

    nf.values.push_back(n.freq);

    fs[1].push_back(nf);

}

void

CepstrumPitchTracker::filter(const double *cep, double *data)

{

    for (int i = 0; i < m_bins; ++i) {

        double v = 0;

        int n = 0;

        // average according to the vertical filter length

        for (int j = -m_vflen/2; j <= m_vflen/2; ++j) {

            int ix = i + m_binFrom + j;

            if (ix >= 0 && ix < m_blockSize) {

                v += cep[ix];

                ++n;

            }

        }

        data[i] = v / n;

    }

}

double

CepstrumPitchTracker::cubicInterpolate(const double y[4], double x)

{

    double a0 = y[3] - y[2] - y[0] + y[1];

    double a1 = y[0] - y[1] - a0;

    double a2 = y[2] - y[0];

    double a3 = y[1];

    return

        a0 * x * x * x +

        a1 * x * x +

        a2 * x +

        a3;

}

double

CepstrumPitchTracker::findInterpolatedPeak(const double *in, int maxbin)

{

    if (maxbin < 2 || maxbin > m_bins - 3) {

        return maxbin;

    }

    double maxval = 0.0;

    double maxidx = maxbin;

    const int divisions = 10;

    double y[4];

    y[0] = in[maxbin-1];

    y[1] = in[maxbin];

    y[2] = in[maxbin+1];

    y[3] = in[maxbin+2];

    for (int i = 0; i < divisions; ++i) {

        double probe = double(i) / double(divisions);

        double value = cubicInterpolate(y, probe);

        if (value > maxval) {

            maxval = value; 

            maxidx = maxbin + probe;

        }

    }

    y[3] = y[2];

    y[2] = y[1];

    y[1] = y[0];

    y[0] = in[maxbin-2];

    for (int i = 0; i < divisions; ++i) {

        double probe = double(i) / double(divisions);

        double value = cubicInterpolate(y, probe);

        if (value > maxval) {

            maxval = value; 

            maxidx = maxbin - 1 + probe;

        }

    }

/*

    std::cerr << "centre = " << maxbin << ": ["

              << in[maxbin-2] << ","

              << in[maxbin-1] << ","

              << in[maxbin] << ","

              << in[maxbin+1] << ","

              << in[maxbin+2] << "] -> " << maxidx << std::endl;

*/

    return maxidx;

}

CepstrumPitchTracker::FeatureSet

CepstrumPitchTracker::process(const float *const *inputBuffers, RealTime timestamp)

{

    FeatureSet fs;

    int bs = m_blockSize;

    int hs = m_blockSize/2 + 1;

    double *rawcep = new double[bs];

    double *io = new double[bs];

    double *logmag = new double[bs];

    // The "inverse symmetric" method. Seems to be the most reliable

    double magmean = 0.0;

    for (int i = 0; i < hs; ++i) {

        double power =

            inputBuffers[0][i*2  ] * inputBuffers[0][i*2  ] +

            inputBuffers[0][i*2+1] * inputBuffers[0][i*2+1];

        double mag = sqrt(power);

        magmean += mag;

        double lm = log(mag + 0.00000001);

        logmag[i] = lm;

        if (i > 0) logmag[bs - i] = lm;

    }

    magmean /= hs;

    double threshold = 0.1; // for magmean

    Vamp::FFT::inverse(bs, logmag, 0, rawcep, io);

    delete[] logmag;

    delete[] io;

    int n = m_bins;

    double *data = new double[n];

    filter(rawcep, data);

    delete[] rawcep;

    double maxval = 0.0;

    int maxbin = -1;

    for (int i = 0; i < n; ++i) {

        if (data[i] > maxval) {

            maxval = data[i];

            maxbin = i;

        }

    }

    if (maxbin < 0) {

        delete[] data;

        return fs;

    }

    double nextPeakVal = 0.0;

    for (int i = 1; i+1 < n; ++i) {

        if (data[i] > data[i-1] &&

            data[i] > data[i+1] &&

            i != maxbin &&

            data[i] > nextPeakVal) {

            nextPeakVal = data[i];

        }

    }

    double cimax = findInterpolatedPeak(data, maxbin);

    double peakfreq = m_inputSampleRate / (cimax + m_binFrom);

    double confidence = 0.0;

    if (nextPeakVal != 0.0) {

        confidence = (maxval - nextPeakVal) * 10.0;

        if (magmean < threshold) confidence = 0.0;

        std::cerr << "magmean = " << magmean << ", confidence = " << confidence << std::endl;

    }

    Hypothesis::Estimate e;

    e.freq = peakfreq;

    e.time = timestamp;

    e.confidence = confidence;

//    m_good.advanceTime();

    for (int i = 0; i < m_possible.size(); ++i) {

//        m_possible[i].advanceTime();

    }

    if (!m_good.accept(e)) {

        int candidate = -1;

        bool accepted = false;

        for (int i = 0; i < m_possible.size(); ++i) {

            if (m_possible[i].accept(e)) {

                if (m_possible[i].getState() == Hypothesis::Satisfied) {

                    accepted = true;

                    candidate = i;

                }

                break;

            }

        }

        if (!accepted) {

            Hypothesis h;

            h.accept(e); //!!! must succeed as h is new, so perhaps there should be a ctor for this

            m_possible.push_back(h);

        }

        if (m_good.getState() == Hypothesis::Expired) {

            addFeaturesFrom(m_good, fs);

        }

        if (m_good.getState() == Hypothesis::Expired ||

            m_good.getState() == Hypothesis::Rejected) {

            if (candidate >= 0) {

                m_good = m_possible[candidate];

            } else {

                m_good = Hypothesis();

            }

        }

        // reap rejected/expired hypotheses from possible list

        Hypotheses toReap = m_possible;

        m_possible.clear();

        for (int i = 0; i < toReap.size(); ++i) {

            Hypothesis h = toReap[i];

            if (h.getState() != Hypothesis::Rejected && 

                h.getState() != Hypothesis::Expired) {

                m_possible.push_back(h);

            }

        }

    }  

    delete[] data;

    return fs;

}

CepstrumPitchTracker::FeatureSet

CepstrumPitchTracker::getRemainingFeatures()

{

    FeatureSet fs;

    if (m_good.getState() == Hypothesis::Satisfied) {

        addFeaturesFrom(m_good, fs);

    }

    return fs;

}