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