Cepstral Pitch Tracker

#include "Cepstrum.h"

    double *rawcep = new double[m_blockSize];

    double magmean = Cepstrum(m_blockSize).process(inputBuffers[0], rawcep);

    MeanFilter(m_vflen).filterSubsequence

        (rawcep, data, m_blockSize, n, m_binFrom);

    double threshold = 0.1; // for magmean

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

/*

    This file is Copyright (c) 2012 Chris Cannam

    Permission is hereby granted, free of charge, to any person

    obtaining a copy of this software and associated documentation

    files (the "Software"), to deal in the Software without

    restriction, including without limitation the rights to use, copy,

    modify, merge, publish, distribute, sublicense, and/or sell copies

    of the Software, and to permit persons to whom the Software is

    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be

    included in all copies or substantial portions of the Software.

    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

    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR

    ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF

    CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION

    WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

*/

#ifndef _CEPSTRUM_H_

#define _CEPSTRUM_H_

#include "vamp-sdk/FFT.h"

#include <cmath>

#include <iostream>

#include <exception>

class Cepstrum

{

public:

    /**

     * Construct a cepstrum converter based on an n-point FFT.

     */

    Cepstrum(int n) : m_n(n) {

	if (n & (n-1)) {

	    throw "N must be a power of two";

	}

    }

    ~Cepstrum() { }

    /**

     * Convert the given frequency-domain data to the cepstral domain.

     *

     * The input must be in the format used for FrequencyDomain data

     * in the Vamp SDK: n/2+1 consecutive pairs of real and imaginary

     * component floats corresponding to bins 0..(n/2) of the FFT

     * output. Thus, n+2 values in total.

     *

     * The output consists of the raw cepstrum of length n.

     *

     * The cepstrum is calculated as the inverse FFT of a

     * synthetically symmetrical base-10 log magnitude spectrum.

     *

     * Returns the mean magnitude of the input spectrum.

     */

    double process(const float *in, double *out) {

	int hs = m_n/2 + 1;

	double *io = new double[m_n];

	double *logmag = new double[m_n];

	double epsilon = 1e-10;

	double magmean = 0.0;

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

	    double power = in[i*2] * in[i*2] + in[i*2+1] * in[i*2+1];

	    double mag = sqrt(power);

	    magmean += mag;

	    logmag[i] = log10(mag + epsilon);

	    if (i > 0) {

		// make the log magnitude spectrum symmetrical

		logmag[m_n - i] = logmag[i];

	    }

	}

	magmean /= hs;

	/*

	std::cerr << "logmags:" << std::endl;

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

	    std::cerr << logmag[i] << " ";

	}

	std::cerr << std::endl;

	*/

	Vamp::FFT::inverse(m_n, logmag, 0, out, io);

	delete[] logmag;

	delete[] io;

	return magmean;

    }

private:

    int m_n;

};

#endif

TESTS := test/test-meanfilter \

	 test/test-cepstrum \

         test/test-peakinterpolator \

	 test/test-notehypothesis

test/test-cepstrum: test/TestCepstrum.o $(OBJECTS)

	$(CXX) -o $@ $^ $(TEST_LDFLAGS)

depend:

		makedepend -Y -fMakefile.inc *.cpp test/*.cpp *.h test/*.h

CepstralPitchTracker.o: CepstralPitchTracker.h NoteHypothesis.h Cepstrum.h

CepstralPitchTracker.o: MeanFilter.h PeakInterpolator.h

test/TestCepstrum.o: Cepstrum.h

test/TestMeanFilter.o: MeanFilter.h

CepstralPitchTracker.o: NoteHypothesis.h

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

/*

    This file is Copyright (c) 2012 Chris Cannam

    Permission is hereby granted, free of charge, to any person

    obtaining a copy of this software and associated documentation

    files (the "Software"), to deal in the Software without

    restriction, including without limitation the rights to use, copy,

    modify, merge, publish, distribute, sublicense, and/or sell copies

    of the Software, and to permit persons to whom the Software is

    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be

    included in all copies or substantial portions of the Software.

    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

    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR

    ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF

    CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION

    WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

*/

#include "Cepstrum.h"

#define BOOST_TEST_DYN_LINK

#define BOOST_TEST_MAIN

#include <boost/test/unit_test.hpp>

BOOST_AUTO_TEST_SUITE(TestCepstrum)

BOOST_AUTO_TEST_CASE(cosine)

{

    // input format is re0, im0, re1, im1...

    float in[] = { 0,0, 10,0, 0,0 };

    double out[4];

    double mm = Cepstrum(4).process(in, out);

    BOOST_CHECK_SMALL(out[0] - (-4.5), 1e-10);

    BOOST_CHECK_EQUAL(out[1], 0);

    BOOST_CHECK_SMALL(out[2] - (-5.5), 1e-10);

    BOOST_CHECK_EQUAL(out[3], 0);

    BOOST_CHECK_EQUAL(mm, 10.0/3.0);

}

BOOST_AUTO_TEST_CASE(symmetry)

{

    // Cepstrum output bins 1..n-1 are symmetric about bin n/2

    float in[] = { 1,2,3,4,5,6,7,8,9,10 };

    double out[8];

    double mm = Cepstrum(8).process(in, out);

    BOOST_CHECK_SMALL(out[1] - out[7], 1e-14);

    BOOST_CHECK_SMALL(out[2] - out[6], 1e-14);

    BOOST_CHECK_SMALL(out[3] - out[5], 1e-14);

}

BOOST_AUTO_TEST_CASE(oneHarmonic)

{

    // input format is re0, im0, re1, im1, re2, im2

    // freq for bin i is i * samplerate / n

    // freqs:        0  sr/n  2sr/n  3sr/n  4sr/n  5sr/n  6sr/n  7sr/n  sr/2

    float in[] = { 0,0,  0,0,  10,0,   0,0,  10,0,   0,0,  10,0,   0,0,  0,0 };

    double out[16];

    double mm = Cepstrum(16).process(in, out);

    BOOST_CHECK_EQUAL(mm, 30.0/9.0);

    // peak is at 8

    BOOST_CHECK(out[8] > 0);

    // odd bins are all zero

    BOOST_CHECK_EQUAL(out[1], 0);

    BOOST_CHECK_EQUAL(out[3], 0);

    BOOST_CHECK_EQUAL(out[5], 0);

    BOOST_CHECK_EQUAL(out[7], 0);

    BOOST_CHECK_EQUAL(out[9], 0);

    BOOST_CHECK_EQUAL(out[11], 0);

    BOOST_CHECK_EQUAL(out[13], 0);

    BOOST_CHECK_EQUAL(out[15], 0);

    // the rest are negative

    BOOST_CHECK(out[0] < 0);

    BOOST_CHECK(out[2] < 0);

    BOOST_CHECK(out[4] < 0);

    BOOST_CHECK(out[6] < 0);

    BOOST_CHECK(out[10] < 0);

    BOOST_CHECK(out[12] < 0);

    BOOST_CHECK(out[14] < 0);

}

BOOST_AUTO_TEST_SUITE_END()