path: root/dom/media/webaudio/blink/Biquad.cpp

/*
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 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1.  Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
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 *     notice, this list of conditions and the following disclaimer in the
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 *     its contributors may be used to endorse or promote products derived
 *     from this software without specific prior written permission.
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 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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#include "Biquad.h"

#include <float.h>
#include <algorithm>
#include <math.h>

namespace WebCore {

Biquad::Biquad()
{
    // Initialize as pass-thru (straight-wire, no filter effect)
    setNormalizedCoefficients(1, 0, 0, 1, 0, 0);

    reset(); // clear filter memory
}

Biquad::~Biquad()
{
}

void Biquad::process(const float* sourceP, float* destP, size_t framesToProcess)
{
    // Create local copies of member variables
    double x1 = m_x1;
    double x2 = m_x2;
    double y1 = m_y1;
    double y2 = m_y2;

    double b0 = m_b0;
    double b1 = m_b1;
    double b2 = m_b2;
    double a1 = m_a1;
    double a2 = m_a2;

    for (size_t i = 0; i < framesToProcess; ++i) {
        // FIXME: this can be optimized by pipelining the multiply adds...
        double x = sourceP[i];
        double y = b0*x + b1*x1 + b2*x2 - a1*y1 - a2*y2;

        destP[i] = y;

        // Update state variables
        x2 = x1;
        x1 = x;
        y2 = y1;
        y1 = y;
    }

    // Avoid introducing a stream of subnormals when input is silent and the
    // tail approaches zero.
    // TODO: Remove this code when Bug 1157635 is fixed.
    if (x1 == 0.0 && x2 == 0.0 && (y1 != 0.0 || y2 != 0.0) &&
        fabs(y1) < FLT_MIN && fabs(y2) < FLT_MIN) {
      // Flush future values to zero (until there is new input).
      y1 = y2 = 0.0;
      // Flush calculated values.
      for (int i = framesToProcess; i-- && fabsf(destP[i]) < FLT_MIN; ) {
        destP[i] = 0.0f;
      }
    }
    // Local variables back to member.
    m_x1 = x1;
    m_x2 = x2;
    m_y1 = y1;
    m_y2 = y2;
}

void Biquad::reset()
{
    m_x1 = m_x2 = m_y1 = m_y2 = 0;
}

void Biquad::setLowpassParams(double cutoff, double resonance)
{
    // Limit cutoff to 0 to 1.
    cutoff = std::max(0.0, std::min(cutoff, 1.0));

    if (cutoff == 1) {
        // When cutoff is 1, the z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    } else if (cutoff > 0) {
        // Compute biquad coefficients for lowpass filter
        resonance = std::max(0.0, resonance); // can't go negative
        double g = pow(10.0, -0.05 * resonance);
        double w0 = M_PI * cutoff;
        double cos_w0 = cos(w0);
        double alpha = 0.5 * sin(w0) * g;

        double b1 = 1.0 - cos_w0;
        double b0 = 0.5 * b1;
        double b2 = b0;
        double a0 = 1.0 + alpha;
        double a1 = -2.0 * cos_w0;
        double a2 = 1.0 - alpha;

        setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
    } else {
        // When cutoff is zero, nothing gets through the filter, so set
        // coefficients up correctly.
        setNormalizedCoefficients(0, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setHighpassParams(double cutoff, double resonance)
{
    // Limit cutoff to 0 to 1.
    cutoff = std::max(0.0, std::min(cutoff, 1.0));

    if (cutoff == 1) {
        // The z-transform is 0.
        setNormalizedCoefficients(0, 0, 0,
                                  1, 0, 0);
    } else if (cutoff > 0) {
        // Compute biquad coefficients for highpass filter
        resonance = std::max(0.0, resonance); // can't go negative
        double g = pow(10.0, -0.05 * resonance);
        double w0 = M_PI * cutoff;
        double cos_w0 = cos(w0);
        double alpha = 0.5 * sin(w0) * g;

        double b1 = -1.0 - cos_w0;
        double b0 = -0.5 * b1;
        double b2 = b0;
        double a0 = 1.0 + alpha;
        double a1 = -2.0 * cos_w0;
        double a2 = 1.0 - alpha;

        setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
    } else {
      // When cutoff is zero, we need to be careful because the above
      // gives a quadratic divided by the same quadratic, with poles
      // and zeros on the unit circle in the same place. When cutoff
      // is zero, the z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setNormalizedCoefficients(double b0, double b1, double b2, double a0, double a1, double a2)
{
    double a0Inverse = 1 / a0;

    m_b0 = b0 * a0Inverse;
    m_b1 = b1 * a0Inverse;
    m_b2 = b2 * a0Inverse;
    m_a1 = a1 * a0Inverse;
    m_a2 = a2 * a0Inverse;
}

void Biquad::setLowShelfParams(double frequency, double dbGain)
{
    // Clip frequencies to between 0 and 1, inclusive.
    frequency = std::max(0.0, std::min(frequency, 1.0));

    double A = pow(10.0, dbGain / 40);

    if (frequency == 1) {
        // The z-transform is a constant gain.
        setNormalizedCoefficients(A * A, 0, 0,
                                  1, 0, 0);
    } else if (frequency > 0) {
        double w0 = M_PI * frequency;
        double S = 1; // filter slope (1 is max value)
        double alpha = 0.5 * sin(w0) * sqrt((A + 1 / A) * (1 / S - 1) + 2);
        double k = cos(w0);
        double k2 = 2 * sqrt(A) * alpha;
        double aPlusOne = A + 1;
        double aMinusOne = A - 1;

        double b0 = A * (aPlusOne - aMinusOne * k + k2);
        double b1 = 2 * A * (aMinusOne - aPlusOne * k);
        double b2 = A * (aPlusOne - aMinusOne * k - k2);
        double a0 = aPlusOne + aMinusOne * k + k2;
        double a1 = -2 * (aMinusOne + aPlusOne * k);
        double a2 = aPlusOne + aMinusOne * k - k2;

        setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
    } else {
        // When frequency is 0, the z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setHighShelfParams(double frequency, double dbGain)
{
    // Clip frequencies to between 0 and 1, inclusive.
    frequency = std::max(0.0, std::min(frequency, 1.0));

    double A = pow(10.0, dbGain / 40);

    if (frequency == 1) {
        // The z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    } else if (frequency > 0) {
        double w0 = M_PI * frequency;
        double S = 1; // filter slope (1 is max value)
        double alpha = 0.5 * sin(w0) * sqrt((A + 1 / A) * (1 / S - 1) + 2);
        double k = cos(w0);
        double k2 = 2 * sqrt(A) * alpha;
        double aPlusOne = A + 1;
        double aMinusOne = A - 1;

        double b0 = A * (aPlusOne + aMinusOne * k + k2);
        double b1 = -2 * A * (aMinusOne + aPlusOne * k);
        double b2 = A * (aPlusOne + aMinusOne * k - k2);
        double a0 = aPlusOne - aMinusOne * k + k2;
        double a1 = 2 * (aMinusOne - aPlusOne * k);
        double a2 = aPlusOne - aMinusOne * k - k2;

        setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
    } else {
        // When frequency = 0, the filter is just a gain, A^2.
        setNormalizedCoefficients(A * A, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setPeakingParams(double frequency, double Q, double dbGain)
{
    // Clip frequencies to between 0 and 1, inclusive.
    frequency = std::max(0.0, std::min(frequency, 1.0));

    // Don't let Q go negative, which causes an unstable filter.
    Q = std::max(0.0, Q);

    double A = pow(10.0, dbGain / 40);

    if (frequency > 0 && frequency < 1) {
        if (Q > 0) {
            double w0 = M_PI * frequency;
            double alpha = sin(w0) / (2 * Q);
            double k = cos(w0);

            double b0 = 1 + alpha * A;
            double b1 = -2 * k;
            double b2 = 1 - alpha * A;
            double a0 = 1 + alpha / A;
            double a1 = -2 * k;
            double a2 = 1 - alpha / A;

            setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
        } else {
            // When Q = 0, the above formulas have problems. If we look at
            // the z-transform, we can see that the limit as Q->0 is A^2, so
            // set the filter that way.
            setNormalizedCoefficients(A * A, 0, 0,
                                      1, 0, 0);
        }
    } else {
        // When frequency is 0 or 1, the z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setAllpassParams(double frequency, double Q)
{
    // Clip frequencies to between 0 and 1, inclusive.
    frequency = std::max(0.0, std::min(frequency, 1.0));

    // Don't let Q go negative, which causes an unstable filter.
    Q = std::max(0.0, Q);

    if (frequency > 0 && frequency < 1) {
        if (Q > 0) {
            double w0 = M_PI * frequency;
            double alpha = sin(w0) / (2 * Q);
            double k = cos(w0);

            double b0 = 1 - alpha;
            double b1 = -2 * k;
            double b2 = 1 + alpha;
            double a0 = 1 + alpha;
            double a1 = -2 * k;
            double a2 = 1 - alpha;

            setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
        } else {
            // When Q = 0, the above formulas have problems. If we look at
            // the z-transform, we can see that the limit as Q->0 is -1, so
            // set the filter that way.
            setNormalizedCoefficients(-1, 0, 0,
                                      1, 0, 0);
        }
    } else {
        // When frequency is 0 or 1, the z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setNotchParams(double frequency, double Q)
{
    // Clip frequencies to between 0 and 1, inclusive.
    frequency = std::max(0.0, std::min(frequency, 1.0));

    // Don't let Q go negative, which causes an unstable filter.
    Q = std::max(0.0, Q);

    if (frequency > 0 && frequency < 1) {
        if (Q > 0) {
            double w0 = M_PI * frequency;
            double alpha = sin(w0) / (2 * Q);
            double k = cos(w0);

            double b0 = 1;
            double b1 = -2 * k;
            double b2 = 1;
            double a0 = 1 + alpha;
            double a1 = -2 * k;
            double a2 = 1 - alpha;

            setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
        } else {
            // When Q = 0, the above formulas have problems. If we look at
            // the z-transform, we can see that the limit as Q->0 is 0, so
            // set the filter that way.
            setNormalizedCoefficients(0, 0, 0,
                                      1, 0, 0);
        }
    } else {
        // When frequency is 0 or 1, the z-transform is 1.
        setNormalizedCoefficients(1, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setBandpassParams(double frequency, double Q)
{
    // No negative frequencies allowed.
    frequency = std::max(0.0, frequency);

    // Don't let Q go negative, which causes an unstable filter.
    Q = std::max(0.0, Q);

    if (frequency > 0 && frequency < 1) {
        double w0 = M_PI * frequency;
        if (Q > 0) {
            double alpha = sin(w0) / (2 * Q);
            double k = cos(w0);

            double b0 = alpha;
            double b1 = 0;
            double b2 = -alpha;
            double a0 = 1 + alpha;
            double a1 = -2 * k;
            double a2 = 1 - alpha;

            setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
        } else {
            // When Q = 0, the above formulas have problems. If we look at
            // the z-transform, we can see that the limit as Q->0 is 1, so
            // set the filter that way.
            setNormalizedCoefficients(1, 0, 0,
                                      1, 0, 0);
        }
    } else {
        // When the cutoff is zero, the z-transform approaches 0, if Q
        // > 0. When both Q and cutoff are zero, the z-transform is
        // pretty much undefined. What should we do in this case?
        // For now, just make the filter 0. When the cutoff is 1, the
        // z-transform also approaches 0.
        setNormalizedCoefficients(0, 0, 0,
                                  1, 0, 0);
    }
}

void Biquad::setZeroPolePairs(const Complex &zero, const Complex &pole)
{
    double b0 = 1;
    double b1 = -2 * zero.real();

    double zeroMag = abs(zero);
    double b2 = zeroMag * zeroMag;

    double a1 = -2 * pole.real();

    double poleMag = abs(pole);
    double a2 = poleMag * poleMag;
    setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
}

void Biquad::setAllpassPole(const Complex &pole)
{
    Complex zero = Complex(1, 0) / pole;
    setZeroPolePairs(zero, pole);
}

void Biquad::getFrequencyResponse(int nFrequencies,
                                  const float* frequency,
                                  float* magResponse,
                                  float* phaseResponse)
{
    // Evaluate the Z-transform of the filter at given normalized
    // frequency from 0 to 1.  (1 corresponds to the Nyquist
    // frequency.)
    //
    // The z-transform of the filter is
    //
    // H(z) = (b0 + b1*z^(-1) + b2*z^(-2))/(1 + a1*z^(-1) + a2*z^(-2))
    //
    // Evaluate as
    //
    // b0 + (b1 + b2*z1)*z1
    // --------------------
    // 1 + (a1 + a2*z1)*z1
    //
    // with z1 = 1/z and z = exp(j*pi*frequency). Hence z1 = exp(-j*pi*frequency)

    // Make local copies of the coefficients as a micro-optimization.
    double b0 = m_b0;
    double b1 = m_b1;
    double b2 = m_b2;
    double a1 = m_a1;
    double a2 = m_a2;

    for (int k = 0; k < nFrequencies; ++k) {
        double omega = -M_PI * frequency[k];
        Complex z = Complex(cos(omega), sin(omega));
        Complex numerator = b0 + (b1 + b2 * z) * z;
        Complex denominator = Complex(1, 0) + (a1 + a2 * z) * z;
        // Strangely enough, using complex division:
        // e.g. Complex response = numerator / denominator;
        // fails on our test machines, yielding infinities and NaNs, so we do
        // things the long way here.
        double n = norm(denominator);
        double r = (real(numerator)*real(denominator) + imag(numerator)*imag(denominator)) / n;
        double i = (imag(numerator)*real(denominator) - real(numerator)*imag(denominator)) / n;
        std::complex<double> response = std::complex<double>(r, i);

        magResponse[k] = static_cast<float>(abs(response));
        phaseResponse[k] = static_cast<float>(atan2(imag(response), real(response)));
    }
}

} // namespace WebCore