michael@0: /*
michael@0:  * Copyright (C) 2010 Google Inc. All rights reserved.
michael@0:  *
michael@0:  * Redistribution and use in source and binary forms, with or without
michael@0:  * modification, are permitted provided that the following conditions
michael@0:  * are met:
michael@0:  *
michael@0:  * 1.  Redistributions of source code must retain the above copyright
michael@0:  *     notice, this list of conditions and the following disclaimer.
michael@0:  * 2.  Redistributions in binary form must reproduce the above copyright
michael@0:  *     notice, this list of conditions and the following disclaimer in the
michael@0:  *     documentation and/or other materials provided with the distribution.
michael@0:  * 3.  Neither the name of Apple Computer, Inc. ("Apple") nor the names of
michael@0:  *     its contributors may be used to endorse or promote products derived
michael@0:  *     from this software without specific prior written permission.
michael@0:  *
michael@0:  * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
michael@0:  * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
michael@0:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
michael@0:  * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
michael@0:  * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
michael@0:  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
michael@0:  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
michael@0:  * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
michael@0:  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
michael@0:  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
michael@0:  */
michael@0: 
michael@0: // For M_PI from cmath
michael@0: #ifdef _MSC_VER
michael@0: #  define _USE_MATH_DEFINES
michael@0: #endif
michael@0: 
michael@0: #include "Biquad.h"
michael@0: 
michael@0: #include <cmath>
michael@0: #include <float.h>
michael@0: #include <algorithm>
michael@0: 
michael@0: namespace WebCore {
michael@0: 
michael@0: Biquad::Biquad()
michael@0: {
michael@0:     // Initialize as pass-thru (straight-wire, no filter effect)
michael@0:     setNormalizedCoefficients(1, 0, 0, 1, 0, 0);
michael@0: 
michael@0:     reset(); // clear filter memory
michael@0: }
michael@0: 
michael@0: Biquad::~Biquad()
michael@0: {
michael@0: }
michael@0: 
michael@0: void Biquad::process(const float* sourceP, float* destP, size_t framesToProcess)
michael@0: {
michael@0:     // Create local copies of member variables
michael@0:     double x1 = m_x1;
michael@0:     double x2 = m_x2;
michael@0:     double y1 = m_y1;
michael@0:     double y2 = m_y2;
michael@0: 
michael@0:     double b0 = m_b0;
michael@0:     double b1 = m_b1;
michael@0:     double b2 = m_b2;
michael@0:     double a1 = m_a1;
michael@0:     double a2 = m_a2;
michael@0: 
michael@0:     for (size_t i = 0; i < framesToProcess; ++i) {
michael@0:         // FIXME: this can be optimized by pipelining the multiply adds...
michael@0:         double x = sourceP[i];
michael@0:         double y = b0*x + b1*x1 + b2*x2 - a1*y1 - a2*y2;
michael@0: 
michael@0:         destP[i] = y;
michael@0: 
michael@0:         // Update state variables
michael@0:         x2 = x1;
michael@0:         x1 = x;
michael@0:         y2 = y1;
michael@0:         y1 = y;
michael@0:     }
michael@0: 
michael@0:     // Avoid introducing a stream of subnormals when input is silent and the
michael@0:     // tail approaches zero.
michael@0:     if (x1 == 0.0 && x2 == 0.0 && (y1 != 0.0 || y2 != 0.0) &&
michael@0:         fabs(y1) < FLT_MIN && fabs(y2) < FLT_MIN) {
michael@0:       // Flush future values to zero (until there is new input).
michael@0:       y1 = y2 = 0.0;
michael@0:       // Flush calculated values.
michael@0:       for (int i = framesToProcess; i-- && fabsf(destP[i]) < FLT_MIN; ) {
michael@0:         destP[i] = 0.0f;
michael@0:       }
michael@0:     }
michael@0:     // Local variables back to member.
michael@0:     m_x1 = x1;
michael@0:     m_x2 = x2;
michael@0:     m_y1 = y1;
michael@0:     m_y2 = y2;
michael@0: }
michael@0: 
michael@0: void Biquad::reset()
michael@0: {
michael@0:     m_x1 = m_x2 = m_y1 = m_y2 = 0;
michael@0: }
michael@0: 
michael@0: void Biquad::setLowpassParams(double cutoff, double resonance)
michael@0: {
michael@0:     // Limit cutoff to 0 to 1.
michael@0:     cutoff = std::max(0.0, std::min(cutoff, 1.0));
michael@0: 
michael@0:     if (cutoff == 1) {
michael@0:         // When cutoff is 1, the z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     } else if (cutoff > 0) {
michael@0:         // Compute biquad coefficients for lowpass filter
michael@0:         resonance = std::max(0.0, resonance); // can't go negative
michael@0:         double g = pow(10.0, 0.05 * resonance);
michael@0:         double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2);
michael@0: 
michael@0:         double theta = M_PI * cutoff;
michael@0:         double sn = 0.5 * d * sin(theta);
michael@0:         double beta = 0.5 * (1 - sn) / (1 + sn);
michael@0:         double gamma = (0.5 + beta) * cos(theta);
michael@0:         double alpha = 0.25 * (0.5 + beta - gamma);
michael@0: 
michael@0:         double b0 = 2 * alpha;
michael@0:         double b1 = 2 * 2 * alpha;
michael@0:         double b2 = 2 * alpha;
michael@0:         double a1 = 2 * -gamma;
michael@0:         double a2 = 2 * beta;
michael@0: 
michael@0:         setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
michael@0:     } else {
michael@0:         // When cutoff is zero, nothing gets through the filter, so set
michael@0:         // coefficients up correctly.
michael@0:         setNormalizedCoefficients(0, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setHighpassParams(double cutoff, double resonance)
michael@0: {
michael@0:     // Limit cutoff to 0 to 1.
michael@0:     cutoff = std::max(0.0, std::min(cutoff, 1.0));
michael@0: 
michael@0:     if (cutoff == 1) {
michael@0:         // The z-transform is 0.
michael@0:         setNormalizedCoefficients(0, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     } else if (cutoff > 0) {
michael@0:         // Compute biquad coefficients for highpass filter
michael@0:         resonance = std::max(0.0, resonance); // can't go negative
michael@0:         double g = pow(10.0, 0.05 * resonance);
michael@0:         double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2);
michael@0: 
michael@0:         double theta = M_PI * cutoff;
michael@0:         double sn = 0.5 * d * sin(theta);
michael@0:         double beta = 0.5 * (1 - sn) / (1 + sn);
michael@0:         double gamma = (0.5 + beta) * cos(theta);
michael@0:         double alpha = 0.25 * (0.5 + beta + gamma);
michael@0: 
michael@0:         double b0 = 2 * alpha;
michael@0:         double b1 = 2 * -2 * alpha;
michael@0:         double b2 = 2 * alpha;
michael@0:         double a1 = 2 * -gamma;
michael@0:         double a2 = 2 * beta;
michael@0: 
michael@0:         setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
michael@0:     } else {
michael@0:       // When cutoff is zero, we need to be careful because the above
michael@0:       // gives a quadratic divided by the same quadratic, with poles
michael@0:       // and zeros on the unit circle in the same place. When cutoff
michael@0:       // is zero, the z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setNormalizedCoefficients(double b0, double b1, double b2, double a0, double a1, double a2)
michael@0: {
michael@0:     double a0Inverse = 1 / a0;
michael@0:     
michael@0:     m_b0 = b0 * a0Inverse;
michael@0:     m_b1 = b1 * a0Inverse;
michael@0:     m_b2 = b2 * a0Inverse;
michael@0:     m_a1 = a1 * a0Inverse;
michael@0:     m_a2 = a2 * a0Inverse;
michael@0: }
michael@0: 
michael@0: void Biquad::setLowShelfParams(double frequency, double dbGain)
michael@0: {
michael@0:     // Clip frequencies to between 0 and 1, inclusive.
michael@0:     frequency = std::max(0.0, std::min(frequency, 1.0));
michael@0: 
michael@0:     double A = pow(10.0, dbGain / 40);
michael@0: 
michael@0:     if (frequency == 1) {
michael@0:         // The z-transform is a constant gain.
michael@0:         setNormalizedCoefficients(A * A, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     } else if (frequency > 0) {
michael@0:         double w0 = M_PI * frequency;
michael@0:         double S = 1; // filter slope (1 is max value)
michael@0:         double alpha = 0.5 * sin(w0) * sqrt((A + 1 / A) * (1 / S - 1) + 2);
michael@0:         double k = cos(w0);
michael@0:         double k2 = 2 * sqrt(A) * alpha;
michael@0:         double aPlusOne = A + 1;
michael@0:         double aMinusOne = A - 1;
michael@0: 
michael@0:         double b0 = A * (aPlusOne - aMinusOne * k + k2);
michael@0:         double b1 = 2 * A * (aMinusOne - aPlusOne * k);
michael@0:         double b2 = A * (aPlusOne - aMinusOne * k - k2);
michael@0:         double a0 = aPlusOne + aMinusOne * k + k2;
michael@0:         double a1 = -2 * (aMinusOne + aPlusOne * k);
michael@0:         double a2 = aPlusOne + aMinusOne * k - k2;
michael@0: 
michael@0:         setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
michael@0:     } else {
michael@0:         // When frequency is 0, the z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setHighShelfParams(double frequency, double dbGain)
michael@0: {
michael@0:     // Clip frequencies to between 0 and 1, inclusive.
michael@0:     frequency = std::max(0.0, std::min(frequency, 1.0));
michael@0: 
michael@0:     double A = pow(10.0, dbGain / 40);
michael@0: 
michael@0:     if (frequency == 1) {
michael@0:         // The z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     } else if (frequency > 0) {
michael@0:         double w0 = M_PI * frequency;
michael@0:         double S = 1; // filter slope (1 is max value)
michael@0:         double alpha = 0.5 * sin(w0) * sqrt((A + 1 / A) * (1 / S - 1) + 2);
michael@0:         double k = cos(w0);
michael@0:         double k2 = 2 * sqrt(A) * alpha;
michael@0:         double aPlusOne = A + 1;
michael@0:         double aMinusOne = A - 1;
michael@0: 
michael@0:         double b0 = A * (aPlusOne + aMinusOne * k + k2);
michael@0:         double b1 = -2 * A * (aMinusOne + aPlusOne * k);
michael@0:         double b2 = A * (aPlusOne + aMinusOne * k - k2);
michael@0:         double a0 = aPlusOne - aMinusOne * k + k2;
michael@0:         double a1 = 2 * (aMinusOne - aPlusOne * k);
michael@0:         double a2 = aPlusOne - aMinusOne * k - k2;
michael@0: 
michael@0:         setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
michael@0:     } else {
michael@0:         // When frequency = 0, the filter is just a gain, A^2.
michael@0:         setNormalizedCoefficients(A * A, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setPeakingParams(double frequency, double Q, double dbGain)
michael@0: {
michael@0:     // Clip frequencies to between 0 and 1, inclusive.
michael@0:     frequency = std::max(0.0, std::min(frequency, 1.0));
michael@0: 
michael@0:     // Don't let Q go negative, which causes an unstable filter.
michael@0:     Q = std::max(0.0, Q);
michael@0: 
michael@0:     double A = pow(10.0, dbGain / 40);
michael@0: 
michael@0:     if (frequency > 0 && frequency < 1) {
michael@0:         if (Q > 0) {
michael@0:             double w0 = M_PI * frequency;
michael@0:             double alpha = sin(w0) / (2 * Q);
michael@0:             double k = cos(w0);
michael@0: 
michael@0:             double b0 = 1 + alpha * A;
michael@0:             double b1 = -2 * k;
michael@0:             double b2 = 1 - alpha * A;
michael@0:             double a0 = 1 + alpha / A;
michael@0:             double a1 = -2 * k;
michael@0:             double a2 = 1 - alpha / A;
michael@0: 
michael@0:             setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
michael@0:         } else {
michael@0:             // When Q = 0, the above formulas have problems. If we look at
michael@0:             // the z-transform, we can see that the limit as Q->0 is A^2, so
michael@0:             // set the filter that way.
michael@0:             setNormalizedCoefficients(A * A, 0, 0,
michael@0:                                       1, 0, 0);
michael@0:         }
michael@0:     } else {
michael@0:         // When frequency is 0 or 1, the z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setAllpassParams(double frequency, double Q)
michael@0: {
michael@0:     // Clip frequencies to between 0 and 1, inclusive.
michael@0:     frequency = std::max(0.0, std::min(frequency, 1.0));
michael@0: 
michael@0:     // Don't let Q go negative, which causes an unstable filter.
michael@0:     Q = std::max(0.0, Q);
michael@0: 
michael@0:     if (frequency > 0 && frequency < 1) {
michael@0:         if (Q > 0) {
michael@0:             double w0 = M_PI * frequency;
michael@0:             double alpha = sin(w0) / (2 * Q);
michael@0:             double k = cos(w0);
michael@0: 
michael@0:             double b0 = 1 - alpha;
michael@0:             double b1 = -2 * k;
michael@0:             double b2 = 1 + alpha;
michael@0:             double a0 = 1 + alpha;
michael@0:             double a1 = -2 * k;
michael@0:             double a2 = 1 - alpha;
michael@0: 
michael@0:             setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
michael@0:         } else {
michael@0:             // When Q = 0, the above formulas have problems. If we look at
michael@0:             // the z-transform, we can see that the limit as Q->0 is -1, so
michael@0:             // set the filter that way.
michael@0:             setNormalizedCoefficients(-1, 0, 0,
michael@0:                                       1, 0, 0);
michael@0:         }
michael@0:     } else {
michael@0:         // When frequency is 0 or 1, the z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setNotchParams(double frequency, double Q)
michael@0: {
michael@0:     // Clip frequencies to between 0 and 1, inclusive.
michael@0:     frequency = std::max(0.0, std::min(frequency, 1.0));
michael@0: 
michael@0:     // Don't let Q go negative, which causes an unstable filter.
michael@0:     Q = std::max(0.0, Q);
michael@0: 
michael@0:     if (frequency > 0 && frequency < 1) {
michael@0:         if (Q > 0) {
michael@0:             double w0 = M_PI * frequency;
michael@0:             double alpha = sin(w0) / (2 * Q);
michael@0:             double k = cos(w0);
michael@0: 
michael@0:             double b0 = 1;
michael@0:             double b1 = -2 * k;
michael@0:             double b2 = 1;
michael@0:             double a0 = 1 + alpha;
michael@0:             double a1 = -2 * k;
michael@0:             double a2 = 1 - alpha;
michael@0: 
michael@0:             setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
michael@0:         } else {
michael@0:             // When Q = 0, the above formulas have problems. If we look at
michael@0:             // the z-transform, we can see that the limit as Q->0 is 0, so
michael@0:             // set the filter that way.
michael@0:             setNormalizedCoefficients(0, 0, 0,
michael@0:                                       1, 0, 0);
michael@0:         }
michael@0:     } else {
michael@0:         // When frequency is 0 or 1, the z-transform is 1.
michael@0:         setNormalizedCoefficients(1, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setBandpassParams(double frequency, double Q)
michael@0: {
michael@0:     // No negative frequencies allowed.
michael@0:     frequency = std::max(0.0, frequency);
michael@0: 
michael@0:     // Don't let Q go negative, which causes an unstable filter.
michael@0:     Q = std::max(0.0, Q);
michael@0: 
michael@0:     if (frequency > 0 && frequency < 1) {
michael@0:         double w0 = M_PI * frequency;
michael@0:         if (Q > 0) {
michael@0:             double alpha = sin(w0) / (2 * Q);
michael@0:             double k = cos(w0);
michael@0:     
michael@0:             double b0 = alpha;
michael@0:             double b1 = 0;
michael@0:             double b2 = -alpha;
michael@0:             double a0 = 1 + alpha;
michael@0:             double a1 = -2 * k;
michael@0:             double a2 = 1 - alpha;
michael@0: 
michael@0:             setNormalizedCoefficients(b0, b1, b2, a0, a1, a2);
michael@0:         } else {
michael@0:             // When Q = 0, the above formulas have problems. If we look at
michael@0:             // the z-transform, we can see that the limit as Q->0 is 1, so
michael@0:             // set the filter that way.
michael@0:             setNormalizedCoefficients(1, 0, 0,
michael@0:                                       1, 0, 0);
michael@0:         }
michael@0:     } else {
michael@0:         // When the cutoff is zero, the z-transform approaches 0, if Q
michael@0:         // > 0. When both Q and cutoff are zero, the z-transform is
michael@0:         // pretty much undefined. What should we do in this case?
michael@0:         // For now, just make the filter 0. When the cutoff is 1, the
michael@0:         // z-transform also approaches 0.
michael@0:         setNormalizedCoefficients(0, 0, 0,
michael@0:                                   1, 0, 0);
michael@0:     }
michael@0: }
michael@0: 
michael@0: void Biquad::setZeroPolePairs(const Complex &zero, const Complex &pole)
michael@0: {
michael@0:     double b0 = 1;
michael@0:     double b1 = -2 * zero.real();
michael@0: 
michael@0:     double zeroMag = abs(zero);
michael@0:     double b2 = zeroMag * zeroMag;
michael@0: 
michael@0:     double a1 = -2 * pole.real();
michael@0: 
michael@0:     double poleMag = abs(pole);
michael@0:     double a2 = poleMag * poleMag;
michael@0:     setNormalizedCoefficients(b0, b1, b2, 1, a1, a2);
michael@0: }
michael@0: 
michael@0: void Biquad::setAllpassPole(const Complex &pole)
michael@0: {
michael@0:     Complex zero = Complex(1, 0) / pole;
michael@0:     setZeroPolePairs(zero, pole);
michael@0: }
michael@0: 
michael@0: void Biquad::getFrequencyResponse(int nFrequencies,
michael@0:                                   const float* frequency,
michael@0:                                   float* magResponse,
michael@0:                                   float* phaseResponse)
michael@0: {
michael@0:     // Evaluate the Z-transform of the filter at given normalized
michael@0:     // frequency from 0 to 1.  (1 corresponds to the Nyquist
michael@0:     // frequency.)
michael@0:     //
michael@0:     // The z-transform of the filter is
michael@0:     //
michael@0:     // H(z) = (b0 + b1*z^(-1) + b2*z^(-2))/(1 + a1*z^(-1) + a2*z^(-2))
michael@0:     //
michael@0:     // Evaluate as
michael@0:     //
michael@0:     // b0 + (b1 + b2*z1)*z1
michael@0:     // --------------------
michael@0:     // 1 + (a1 + a2*z1)*z1
michael@0:     //
michael@0:     // with z1 = 1/z and z = exp(j*pi*frequency). Hence z1 = exp(-j*pi*frequency)
michael@0: 
michael@0:     // Make local copies of the coefficients as a micro-optimization.
michael@0:     double b0 = m_b0;
michael@0:     double b1 = m_b1;
michael@0:     double b2 = m_b2;
michael@0:     double a1 = m_a1;
michael@0:     double a2 = m_a2;
michael@0:     
michael@0:     for (int k = 0; k < nFrequencies; ++k) {
michael@0:         double omega = -M_PI * frequency[k];
michael@0:         Complex z = Complex(cos(omega), sin(omega));
michael@0:         Complex numerator = b0 + (b1 + b2 * z) * z;
michael@0:         Complex denominator = Complex(1, 0) + (a1 + a2 * z) * z;
michael@0:         Complex response = numerator / denominator;
michael@0:         magResponse[k] = static_cast<float>(abs(response));
michael@0:         phaseResponse[k] = static_cast<float>(atan2(imag(response), real(response)));
michael@0:     }
michael@0: }
michael@0: 
michael@0: } // namespace WebCore
michael@0: