PeriodicWave.cpp   [plain text]

/*
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#include "config.h"

#if ENABLE(WEB_AUDIO)

#include "PeriodicWave.h"

#include "FFTFrame.h"
#include "VectorMath.h"
#include <algorithm>

const unsigned PeriodicWaveSize = 4096; // This must be a power of two.
const unsigned NumberOfRanges = 36; // There should be 3 * log2(PeriodicWaveSize) 1/3 octave ranges.
const float CentsPerRange = 1200 / 3; // 1/3 Octave.

namespace WebCore {
    
using namespace VectorMath;

Ref<PeriodicWave> PeriodicWave::create(float sampleRate, Float32Array& real, Float32Array& imaginary)
{
    ASSERT(real.length() == imaginary.length());

    auto waveTable = adoptRef(*new PeriodicWave(sampleRate));
    waveTable->createBandLimitedTables(real.data(), imaginary.data(), real.length());
    return waveTable;
}

Ref<PeriodicWave> PeriodicWave::createSine(float sampleRate)
{
    Ref<PeriodicWave> waveTable = adoptRef(*new PeriodicWave(sampleRate));
    waveTable->generateBasicWaveform(Type::Sine);
    return waveTable;
}

Ref<PeriodicWave> PeriodicWave::createSquare(float sampleRate)
{
    Ref<PeriodicWave> waveTable = adoptRef(*new PeriodicWave(sampleRate));
    waveTable->generateBasicWaveform(Type::Square);
    return waveTable;
}

Ref<PeriodicWave> PeriodicWave::createSawtooth(float sampleRate)
{
    Ref<PeriodicWave> waveTable = adoptRef(*new PeriodicWave(sampleRate));
    waveTable->generateBasicWaveform(Type::Sawtooth);
    return waveTable;
}

Ref<PeriodicWave> PeriodicWave::createTriangle(float sampleRate)
{
    Ref<PeriodicWave> waveTable = adoptRef(*new PeriodicWave(sampleRate));
    waveTable->generateBasicWaveform(Type::Triangle);
    return waveTable;
}

PeriodicWave::PeriodicWave(float sampleRate)
    : m_sampleRate(sampleRate)
    , m_periodicWaveSize(PeriodicWaveSize)
    , m_numberOfRanges(NumberOfRanges)
    , m_centsPerRange(CentsPerRange)
{
    float nyquist = 0.5 * m_sampleRate;
    m_lowestFundamentalFrequency = nyquist / maxNumberOfPartials();
    m_rateScale = m_periodicWaveSize / m_sampleRate;
}

void PeriodicWave::waveDataForFundamentalFrequency(float fundamentalFrequency, float* &lowerWaveData, float* &higherWaveData, float& tableInterpolationFactor)
{
    // Negative frequencies are allowed, in which case we alias to the positive frequency.
    fundamentalFrequency = fabsf(fundamentalFrequency);

    // Calculate the pitch range.
    float ratio = fundamentalFrequency > 0 ? fundamentalFrequency / m_lowestFundamentalFrequency : 0.5;
    float centsAboveLowestFrequency = log2f(ratio) * 1200;

    // Add one to round-up to the next range just in time to truncate partials before aliasing occurs.
    float pitchRange = 1 + centsAboveLowestFrequency / m_centsPerRange;

    pitchRange = std::max(pitchRange, 0.0f);
    pitchRange = std::min(pitchRange, static_cast<float>(m_numberOfRanges - 1));

    // The words "lower" and "higher" refer to the table data having the lower and higher numbers of partials.
    // It's a little confusing since the range index gets larger the more partials we cull out.
    // So the lower table data will have a larger range index.
    unsigned rangeIndex1 = static_cast<unsigned>(pitchRange);
    unsigned rangeIndex2 = rangeIndex1 < m_numberOfRanges - 1 ? rangeIndex1 + 1 : rangeIndex1;

    lowerWaveData = m_bandLimitedTables[rangeIndex2]->data();
    higherWaveData = m_bandLimitedTables[rangeIndex1]->data();
    
    // Ranges from 0 -> 1 to interpolate between lower -> higher.
    tableInterpolationFactor = pitchRange - rangeIndex1;
}

unsigned PeriodicWave::maxNumberOfPartials() const
{
    return m_periodicWaveSize / 2;
}

unsigned PeriodicWave::numberOfPartialsForRange(unsigned rangeIndex) const
{
    // Number of cents below nyquist where we cull partials.
    float centsToCull = rangeIndex * m_centsPerRange;

    // A value from 0 -> 1 representing what fraction of the partials to keep.
    float cullingScale = pow(2, -centsToCull / 1200);

    // The very top range will have all the partials culled.
    unsigned numberOfPartials = cullingScale * maxNumberOfPartials();

    return numberOfPartials;
}

// Convert into time-domain wave tables.
// One table is created for each range for non-aliasing playback at different playback rates.
// Thus, higher ranges have more high-frequency partials culled out.
void PeriodicWave::createBandLimitedTables(const float* realData, const float* imagData, unsigned numberOfComponents)
{
    float normalizationScale = 1;

    unsigned fftSize = m_periodicWaveSize;
    unsigned halfSize = fftSize / 2;
    unsigned i;
    
    numberOfComponents = std::min(numberOfComponents, halfSize);

    m_bandLimitedTables.reserveCapacity(m_numberOfRanges);

    for (unsigned rangeIndex = 0; rangeIndex < m_numberOfRanges; ++rangeIndex) {
        // This FFTFrame is used to cull partials (represented by frequency bins).
        FFTFrame frame(fftSize);
        float* realP = frame.realData();
        float* imagP = frame.imagData();

        // Copy from loaded frequency data and scale.
        float scale = fftSize;
        vsmul(realData, 1, &scale, realP, 1, numberOfComponents);
        vsmul(imagData, 1, &scale, imagP, 1, numberOfComponents);

        // If fewer components were provided than 1/2 FFT size, then clear the remaining bins.
        for (i = numberOfComponents; i < halfSize; ++i) {
            realP[i] = 0;
            imagP[i] = 0;
        }
        
        // Generate complex conjugate because of the way the inverse FFT is defined.
        float minusOne = -1;
        vsmul(imagP, 1, &minusOne, imagP, 1, halfSize);

        // Find the starting bin where we should start culling.
        // We need to clear out the highest frequencies to band-limit the waveform.
        unsigned numberOfPartials = numberOfPartialsForRange(rangeIndex);

        // Cull the aliasing partials for this pitch range.
        for (i = numberOfPartials + 1; i < halfSize; ++i) {
            realP[i] = 0;
            imagP[i] = 0;
        }
        // Clear packed-nyquist if necessary.
        if (numberOfPartials < halfSize)
            imagP[0] = 0;

        // Clear any DC-offset.
        realP[0] = 0;

        // Create the band-limited table.
        m_bandLimitedTables.append(std::make_unique<AudioFloatArray>(m_periodicWaveSize));

        // Apply an inverse FFT to generate the time-domain table data.
        float* data = m_bandLimitedTables[rangeIndex]->data();
        frame.doInverseFFT(data);

        // For the first range (which has the highest power), calculate its peak value then compute normalization scale.
        if (!rangeIndex) {
            float maxValue;
            vmaxmgv(data, 1, &maxValue, m_periodicWaveSize);

            if (maxValue)
                normalizationScale = 1.0f / maxValue;
        }

        // Apply normalization scale.
        vsmul(data, 1, &normalizationScale, data, 1, m_periodicWaveSize);          
    }
}

void PeriodicWave::generateBasicWaveform(Type shape)
{
    unsigned fftSize = periodicWaveSize();
    unsigned halfSize = fftSize / 2;

    AudioFloatArray real(halfSize);
    AudioFloatArray imag(halfSize);
    float* realP = real.data();
    float* imagP = imag.data();

    // Clear DC and Nyquist.
    realP[0] = 0;
    imagP[0] = 0;

    for (unsigned n = 1; n < halfSize; ++n) {
        float omega = 2 * piFloat * n;
        float invOmega = 1 / omega;

        // Fourier coefficients according to standard definition.
        float a; // Coefficient for cos().
        float b; // Coefficient for sin().

        // Calculate Fourier coefficients depending on the shape.
        // Note that the overall scaling (magnitude) of the waveforms is normalized in createBandLimitedTables().
        switch (shape) {
        case Type::Sine:
            // Standard sine wave function.
            a = 0;
            b = (n == 1) ? 1 : 0;
            break;
        case Type::Square:
            // Square-shaped waveform with the first half its maximum value and the second half its minimum value.
            a = 0;
            b = invOmega * ((n & 1) ? 2 : 0);
            break;
        case Type::Sawtooth:
            // Sawtooth-shaped waveform with the first half ramping from zero to maximum and the second half from minimum to zero.
            a = 0;
            b = -invOmega * cos(0.5 * omega);
            break;
        case Type::Triangle:
            // Triangle-shaped waveform going from its maximum value to its minimum value then back to the maximum value.
            a = (4 - 4 * cos(0.5 * omega)) / (n * n * piFloat * piFloat);
            b = 0;
            break;
        }

        realP[n] = a;
        imagP[n] = b;
    }

    createBandLimitedTables(realP, imagP, halfSize);
}

} // namespace WebCore

#endif // ENABLE(WEB_AUDIO)