/* Copyright (c) 2013 The Chromium OS Authors. All rights reserved. * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ /* Copyright (C) 2010 Google Inc. All rights reserved. * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE.WEBKIT file. */ #include <math.h> #include "biquad.h" #ifndef max #define max(a, b) ({ __typeof__(a) _a = (a); \ __typeof__(b) _b = (b); \ _a > _b ? _a : _b; }) #endif #ifndef min #define min(a, b) ({ __typeof__(a) _a = (a); \ __typeof__(b) _b = (b); \ _a < _b ? _a : _b; }) #endif #ifndef M_PI #define M_PI 3.14159265358979323846 #endif static void set_coefficient(struct biquad *bq, double b0, double b1, double b2, double a0, double a1, double a2) { double a0_inv = 1 / a0; bq->b0 = b0 * a0_inv; bq->b1 = b1 * a0_inv; bq->b2 = b2 * a0_inv; bq->a1 = a1 * a0_inv; bq->a2 = a2 * a0_inv; } static void biquad_lowpass(struct biquad *bq, double cutoff, double resonance) { /* Limit cutoff to 0 to 1. */ cutoff = max(0.0, min(cutoff, 1.0)); if (cutoff == 1) { /* When cutoff is 1, the z-transform is 1. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); } else if (cutoff > 0) { /* Compute biquad coefficients for lowpass filter */ resonance = max(0.0, resonance); /* can't go negative */ double g = pow(10.0, 0.05 * resonance); double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2); double theta = M_PI * cutoff; double sn = 0.5 * d * sin(theta); double beta = 0.5 * (1 - sn) / (1 + sn); double gamma = (0.5 + beta) * cos(theta); double alpha = 0.25 * (0.5 + beta - gamma); double b0 = 2 * alpha; double b1 = 2 * 2 * alpha; double b2 = 2 * alpha; double a1 = 2 * -gamma; double a2 = 2 * beta; set_coefficient(bq, b0, b1, b2, 1, a1, a2); } else { /* When cutoff is zero, nothing gets through the filter, so set * coefficients up correctly. */ set_coefficient(bq, 0, 0, 0, 1, 0, 0); } } static void biquad_highpass(struct biquad *bq, double cutoff, double resonance) { /* Limit cutoff to 0 to 1. */ cutoff = max(0.0, min(cutoff, 1.0)); if (cutoff == 1) { /* The z-transform is 0. */ set_coefficient(bq, 0, 0, 0, 1, 0, 0); } else if (cutoff > 0) { /* Compute biquad coefficients for highpass filter */ resonance = max(0.0, resonance); /* can't go negative */ double g = pow(10.0, 0.05 * resonance); double d = sqrt((4 - sqrt(16 - 16 / (g * g))) / 2); double theta = M_PI * cutoff; double sn = 0.5 * d * sin(theta); double beta = 0.5 * (1 - sn) / (1 + sn); double gamma = (0.5 + beta) * cos(theta); double alpha = 0.25 * (0.5 + beta + gamma); double b0 = 2 * alpha; double b1 = 2 * -2 * alpha; double b2 = 2 * alpha; double a1 = 2 * -gamma; double a2 = 2 * beta; set_coefficient(bq, b0, b1, b2, 1, 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. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); } } static void biquad_bandpass(struct biquad *bq, double frequency, double Q) { /* No negative frequencies allowed. */ frequency = max(0.0, frequency); /* Don't let Q go negative, which causes an unstable filter. */ Q = 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; set_coefficient(bq, 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. */ set_coefficient(bq, 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. */ set_coefficient(bq, 0, 0, 0, 1, 0, 0); } } static void biquad_lowshelf(struct biquad *bq, double frequency, double db_gain) { /* Clip frequencies to between 0 and 1, inclusive. */ frequency = max(0.0, min(frequency, 1.0)); double A = pow(10.0, db_gain / 40); if (frequency == 1) { /* The z-transform is a constant gain. */ set_coefficient(bq, 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 a_plus_one = A + 1; double a_minus_one = A - 1; double b0 = A * (a_plus_one - a_minus_one * k + k2); double b1 = 2 * A * (a_minus_one - a_plus_one * k); double b2 = A * (a_plus_one - a_minus_one * k - k2); double a0 = a_plus_one + a_minus_one * k + k2; double a1 = -2 * (a_minus_one + a_plus_one * k); double a2 = a_plus_one + a_minus_one * k - k2; set_coefficient(bq, b0, b1, b2, a0, a1, a2); } else { /* When frequency is 0, the z-transform is 1. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); } } static void biquad_highshelf(struct biquad *bq, double frequency, double db_gain) { /* Clip frequencies to between 0 and 1, inclusive. */ frequency = max(0.0, min(frequency, 1.0)); double A = pow(10.0, db_gain / 40); if (frequency == 1) { /* The z-transform is 1. */ set_coefficient(bq, 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 a_plus_one = A + 1; double a_minus_one = A - 1; double b0 = A * (a_plus_one + a_minus_one * k + k2); double b1 = -2 * A * (a_minus_one + a_plus_one * k); double b2 = A * (a_plus_one + a_minus_one * k - k2); double a0 = a_plus_one - a_minus_one * k + k2; double a1 = 2 * (a_minus_one - a_plus_one * k); double a2 = a_plus_one - a_minus_one * k - k2; set_coefficient(bq, b0, b1, b2, a0, a1, a2); } else { /* When frequency = 0, the filter is just a gain, A^2. */ set_coefficient(bq, A * A, 0, 0, 1, 0, 0); } } static void biquad_peaking(struct biquad *bq, double frequency, double Q, double db_gain) { /* Clip frequencies to between 0 and 1, inclusive. */ frequency = max(0.0, min(frequency, 1.0)); /* Don't let Q go negative, which causes an unstable filter. */ Q = max(0.0, Q); double A = pow(10.0, db_gain / 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; set_coefficient(bq, 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. */ set_coefficient(bq, A * A, 0, 0, 1, 0, 0); } } else { /* When frequency is 0 or 1, the z-transform is 1. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); } } static void biquad_notch(struct biquad *bq, double frequency, double Q) { /* Clip frequencies to between 0 and 1, inclusive. */ frequency = max(0.0, min(frequency, 1.0)); /* Don't let Q go negative, which causes an unstable filter. */ Q = 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; set_coefficient(bq, 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. */ set_coefficient(bq, 0, 0, 0, 1, 0, 0); } } else { /* When frequency is 0 or 1, the z-transform is 1. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); } } static void biquad_allpass(struct biquad *bq, double frequency, double Q) { /* Clip frequencies to between 0 and 1, inclusive. */ frequency = max(0.0, min(frequency, 1.0)); /* Don't let Q go negative, which causes an unstable filter. */ Q = 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; set_coefficient(bq, 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. */ set_coefficient(bq, -1, 0, 0, 1, 0, 0); } } else { /* When frequency is 0 or 1, the z-transform is 1. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); } } void biquad_set(struct biquad *bq, enum biquad_type type, double freq, double Q, double gain) { /* Default is an identity filter. Also clear history values. */ set_coefficient(bq, 1, 0, 0, 1, 0, 0); bq->x1 = 0; bq->x2 = 0; bq->y1 = 0; bq->y2 = 0; switch (type) { case BQ_LOWPASS: biquad_lowpass(bq, freq, Q); break; case BQ_HIGHPASS: biquad_highpass(bq, freq, Q); break; case BQ_BANDPASS: biquad_bandpass(bq, freq, Q); break; case BQ_LOWSHELF: biquad_lowshelf(bq, freq, gain); break; case BQ_HIGHSHELF: biquad_highshelf(bq, freq, gain); break; case BQ_PEAKING: biquad_peaking(bq, freq, Q, gain); break; case BQ_NOTCH: biquad_notch(bq, freq, Q); break; case BQ_ALLPASS: biquad_allpass(bq, freq, Q); break; case BQ_NONE: break; } }