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brickworks/include/bw_iir2.h

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/*
* Brickworks
*
* Copyright (C) 2025 Orastron Srl unipersonale
*
* Brickworks is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, version 3 of the License.
*
* Brickworks is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Brickworks. If not, see <http://www.gnu.org/licenses/>.
*
* File author: Stefano D'Angelo
*/
/*!
* module_type {{{ utility }}}
* version {{{ 1.0.0 }}}
* requires {{{ bw_common bw_math }}}
* description {{{
* Lightweight and fast second-order IIR filter (biquad) in TDF-II form.
*
* This is not a regular DSP module, as it exposes state and coefficients,
* and it's not appropriate for time-varying operation. If you need that,
* check out [bw_ap2](bw_ap2), [bw_hs2](bw_hs2), [bw_ls2](bw_ls2),
* [bw_mm2](bw_mm2), [bw_notch](bw_notch), [bw_peak](bw_peak), and
* [bw_svf](bw_svf).
* }}}
* changelog {{{
* <ul>
* <li>Version <strong>1.0.0</strong>:
* <ul>
* <li>First release.</li>
* </ul>
* </li>
* </ul>
* }}}
*/
#ifndef BW_IIR2_H
#define BW_IIR2_H
#ifdef BW_INCLUDE_WITH_QUOTES
# include "bw_common.h"
#else
# include <bw_common.h>
#endif
#if !defined(BW_CXX_NO_EXTERN_C) && defined(__cplusplus)
extern "C" {
#endif
/*** Public API ***/
/*! api {{{
* #### bw_iir2_reset()
* ```>>> */
static inline void bw_iir2_reset(
float x_0,
float * BW_RESTRICT y_0,
float * BW_RESTRICT s1_0,
float * BW_RESTRICT s2_0,
float b0,
float b1,
float b2,
float a1,
float a2);
/*! <<<```
* Computes and puts the initial output in `y_0` and the initial states in
* `s1_0` and `s2_0`, given the initial input `x_0` and coefficients `b0`,
* `b1`, `b2`, `a1`, and `a2`.
*
* The given coefficients must describe a stable filter.
*
* #### bw_iir2_reset_multi()
* ```>>> */
static inline void bw_iir2_reset_multi(
const float * x_0,
float * y_0,
float * BW_RESTRICT s1_0,
float * s2_0,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_channels);
/*! <<<```
* Computes and puts each of the `n_channels` initial outputs in `y_0` and
* initial states in `s1_0` and `s2_0`, given the corresponding initial
* inputs `x_0` and coefficients `b0`, `b1`, `b2`, `a1`, and `a2`.
*
* `y_0` and/or `s_0` may be `BW_NULL`, in which case the corresponding
* values are not written anywhere.
*
* The given coefficients must describe a stable filter.
*
* #### bw_iir2_process1()
* ```>>> */
static inline void bw_iir2_process1(
float x,
float * BW_RESTRICT y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2);
/*! <<<```
* Processes one input sample `x` using coefficients `b0`, `b1`, `b2`, `a1`,
* and `a2`. The output sample and next states value are put in `y` and
* `s1`/`s2` respectively.
*
* The given coefficients must describe a stable filter.
*
* #### bw_iir2_process()
* ```>>> */
static inline void bw_iir2_process(
const float * x,
float * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_samples);
/*! <<<```
* Processes the first `n_samples` of the input buffer `x` and fills the
* first `n_samples` of the output buffer `y`, while using coefficients `b0`,
* `b1`, `b2`, `a1`, and `a2`. The next state values are put in `s1` and
* `s2`.
*
* The given coefficients must describe a stable filter.
*
* #### bw_iir2_process_multi()
* ```>>> */
static inline void bw_iir2_process_multi(
const float * const * x,
float * const * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_channels,
size_t n_samples);
/*! <<<```
* Processes the first `n_samples` of the `n_channels` input buffers `x` and
* fills the first `n_samples` of the `n_channels` output buffers `y`, while
* using coefficients `b0`, `b1`, `b2`, `a1`, and `a2`. The next `n_channels`
* state values are put in `s1` and `s2`.
*
* The given coefficients must describe a stable filter.
*
* #### bw_iir2_coeffs_ap2()
* ```>>> */
static inline void bw_iir2_coeffs_ap2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1`, and `a2`
* resulting in a second-order allpass filter (180° shift at cutoff,
* approaching 360° shift at high frequencies) with unitary gain, using the
* bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be positive), the `cutoff` frequency
* (Hz, in [`1e-6f`, `1e12f`]), and the quality factor `Q` (in [`1e-6f`,
* `1e6f`]). If `prewarp_freq` is `0`, then the prewarping frequency matches
* `cutoff`, otherwise the value specified by `prewarp_freq` (Hz, in
* [`1e-6f`, `1e12f`], however interally limited to avoid instability) is
* used.
*
* #### bw_iir2_coeffs_bp2()
* ```>>> */
static inline void bw_iir2_coeffs_bp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1`, and `a2`
* resulting in a second-order bandpass filter (6 dB/oct) with peak gain
* `Q` (linear gain), using the bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, in [`1e-6f`, `1e12f`]), and the quality factor `Q` (in
* [`1e-6f`, `1e6f`]). If `prewarp_freq` is `0`, then the prewarping
* frequency matches `cutoff`, otherwise the value specified by
* `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally limited to
* avoid instability) is used.
*
* #### bw_iir2_coeffs_hp2()
* ```>>> */
static inline void bw_iir2_coeffs_hp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1`, and `a2`
* resulting in a second-order highpass filter (12 dB/oct) with gain
* asymptotically approaching unity as frequency increases, using the
* bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, in [`1e-6f`, `1e12f`]), and the quality factor `Q` (in
* [`1e-6f`, `1e6f`]). If `prewarp_freq` is `0`, then the prewarping
* frequency matches `cutoff`, otherwise the value specified by
* `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally limited to
* avoid instability) is used.
*
* #### bw_iir2_coeffs_hs2()
* ```>>> */
static inline void bw_iir2_coeffs_hs2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
char high_gain_dB,
float high_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1,` and `a2`
* resulting in a second-order high shelf filter (12 dB/oct) with unitary DC
* gain, using the bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, must be finite and positive), the quality factor `Q` (in
* [`1e-6f`, `1e6f`]), and the high-frequency gain `high_gain`, either as
* linear gain (in [`1e-30f`, `1e30f`]) if `high_gain_dB` is `0`, or
* otherwise in dB (in [`-600.f`, `600.f`]). If `prewarp_freq` is `0`, then
* the prewarpingfrequency matches `cutoff`, otherwise the value specified by
* `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally limited to
* avoid instability) is used.
*
* `cutoff * bw_sqrtf(bw_sqrtf(high_gain))` must be in [`1e-6f`, `1e12f`],
* where `high_gain` is expressed as linear gain.
*
* #### bw_iir2_coeffs_lp2()
* ```>>> */
static inline void bw_iir2_coeffs_lp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1`, and `a2`
* resulting in a second-order lowpass filter (12 dB/oct) with unitary DC
* gain, using the bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, in [`1e-6f`, `1e12f`]), and the quality factor `Q` (in
* [`1e-6f`, `1e6f`]). If `prewarp_freq` is `0`, then the prewarping
* frequency matches `cutoff`, otherwise the value specified by
* `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally limited to
* avoid instability) is used.
*
* #### bw_iir2_coeffs_ls2()
* ```>>> */
static inline void bw_iir2_coeffs_ls2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
char dc_gain_dB,
float dc_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1,` and `a2`
* resulting in a second-order low shelf filter (12 dB/oct) with gain
* asymptotically approaching unity as frequency increases, using the
* bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, must be finite and positive), the quality factor `Q` (in
* [`1e-6f`, `1e6f`]), and the `dc_gain`, either as linear gain (in
* [`1e-30f`, `1e30f`]) if `high_gain_dB` is `0`, or otherwise in dB (in
* [`-600.f`, `600.f`]). If `prewarp_freq` is `0`, then the prewarping
* frequency matches `cutoff`, otherwise the value specified by
* `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally limited to
* avoid instability) is used.
*
* `cutoff * bw_rpcf(bw_sqrtf(bw_sqrtf(dc_gain)))` must be in [`1e-6f`,
* `1e12f`], where `dc_gain` is expressed as linear gain.
*
* #### bw_iir2_coeffs_mm2()
* ```>>> */
static inline void bw_iir2_coeffs_mm2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float coeff_x,
float coeff_lp,
float coeff_bp,
float coeff_hp,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1`, and `a2`
* resulting in a second-order filter implementing an approximation of the
* Laplace-domain transfer function
*
* > H(s) = coeff\_x + (coeff\_hp s^2 + 2 pi fc s coeff\_bp
* > + (2 pi fc)^2 coeff\_lp) / (s^2 + 2 pi fc / Q s + (2 pi fc)^2)
*
* where fc is the cutoff frequency and Q is the quality factor, using the
* bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, in [`1e-6f`, `1e12f`]), the quality factor `Q` (in
* [`1e-6f`, `1e6f`]), and output coefficients `coeff_x`, `coeff_lp`,
* `coeff_bp`, `coeff_hp` (all must be finite). If `prewarp_freq` is `0`,
* then the prewarping frequency matches `cutoff`, otherwise the value
* specified by `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally
* limited to avoid instability) is used.
*
* #### bw_iir2_coeffs_notch()
* ```>>> */
static inline void bw_iir2_coeffs_notch(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, `b2`, `a1`, and `a2`
* resulting in a second-order notch filter with unitary gain at DC and
* asymptotically as frequency increases, and null gain at cutoff frequency,
* using the bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the `cutoff`
* frequency (Hz, in [`1e-6f`, `1e12f`]), and the quality factor `Q` (in
* [`1e-6f`, `1e6f`]). If `prewarp_freq` is `0`, then the prewarping
* frequency matches `cutoff`, otherwise the value specified by
* `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally limited to
* avoid instability) is used.
*
* #### bw_iir2_coeffs_peak()
* ```>>> */
static inline void bw_iir2_coeffs_peak(
float sample_rate,
float cutoff,
char use_bandwidth,
float Q_bandwidth,
char prewarp_at_cutoff,
float prewarp_freq,
char peak_gain_dB,
float peak_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2);
/*! <<<```
* Computes and puts coefficient values in `b0`, `b1`, and `a1` resulting in
* a second-order peak filter with unitary gain at DC and asymptotically as
* frequency increases, using the bilinear transform with prewarping.
*
* It takes the `sample_rate` (Hz, must be finite and positive), the
* `cutoff` frequency (Hz, in [`1e-6f`, `1e12f`]), and the `peak_gain`,
* either as linear gain (in [`1e-30f`, `1e30f`]) if `peak_gain_dB` is `0`,
* or otherwise in dB (in [`-600.f`, `600.f`]). `Q_bandwidth` indicates
* either the quality factor (in [`1e-6f`, `1e6f`]) if `use_bandwidth` is
* `0`, or otherwise the bandwidth (octaves, in [`1e-6f`, `90.f`]),
* designating the distance between midpoint gain frequencies (i.e.,
* frequencies with gain = peak gain / 2 in dB terms). If `prewarp_freq` is
* `0`, then the prewarping frequency matches `cutoff`, otherwise the value
* specified by `prewarp_freq` (Hz, in [`1e-6f`, `1e12f`], however interally
* limited to avoid instability) is used.
*
* If `use_bandwidth` is non-`0`, then `bw_sqrtf(bw_pow2f(Q_bandwidth) *
* peak_gain) * bw_rcpf(bw_pow2f(Q_bandwidth) - 1.f)` must be in [`1e-6f`,
* `1e6f`], where `peak_gain` is expressed as linear gain.
* }}} */
#if !defined(BW_CXX_NO_EXTERN_C) && defined(__cplusplus)
}
#endif
/*** Implementation ***/
/* WARNING: This part of the file is not part of the public API. Its content may
* change at any time in future versions. Please, do not use it directly. */
#ifdef BW_INCLUDE_WITH_QUOTES
# include "bw_math.h"
#else
# include <bw_math.h>
#endif
#if !defined(BW_CXX_NO_EXTERN_C) && defined(__cplusplus)
extern "C" {
#endif
static inline void bw_iir2_assert_valid_coeffs(
float b0,
float b1,
float b2,
float a1,
float a2) {
#ifndef BW_NO_DEBUG
BW_ASSERT(bw_is_finite(b0));
BW_ASSERT(bw_is_finite(b1));
BW_ASSERT(bw_is_finite(b2));
BW_ASSERT(bw_is_finite(a1));
BW_ASSERT(bw_is_finite(a2));
BW_ASSERT_DEEP(bw_absf(a1) <= 2.f && a2 >= bw_absf(a1) - 1.f && (a2 <= 0.25f * (a1 * a1) || 1.f - 0.25f * (a1 * a1) >= 4.f * (a2 - 0.25f * (a1 * a1)) * (a2 - 0.25f * (a1 * a1))));
#else
(void)b0;
(void)b1;
(void)b2;
(void)a1;
(void)a2;
#endif
}
static inline void bw_iir2_reset(
float x_0,
float * BW_RESTRICT y_0,
float * BW_RESTRICT s1_0,
float * BW_RESTRICT s2_0,
float b0,
float b1,
float b2,
float a1,
float a2) {
BW_ASSERT(bw_is_finite(x_0));
BW_ASSERT(y_0 != BW_NULL);
BW_ASSERT(s1_0 != BW_NULL);
BW_ASSERT(s2_0 != BW_NULL);
BW_ASSERT(y_0 != s1_0);
BW_ASSERT(y_0 != s2_0);
BW_ASSERT(s1_0 != s2_0);
bw_iir2_assert_valid_coeffs(b0, b1, b2, a1, a2);
if (a1 + a2 == -1.f) {
*y_0 = 0.f;
*s1_0 = 0.f;
*s2_0 = 0.f;
} else {
const float d = bw_rcpf(1.f + a1 + a2);
const float k = d * x_0;
*y_0 = k * (b0 + b1 + b2);
*s1_0 = k * (b1 + b2 - b0 * (a1 + a2));
*s2_0 = k * (b2 + b2 * a1 - a2 * (b0 + b1));
}
BW_ASSERT(bw_is_finite(*y_0));
BW_ASSERT(bw_is_finite(*s1_0));
BW_ASSERT(bw_is_finite(*s2_0));
}
static inline void bw_iir2_reset_multi(
const float * x_0,
float * y_0,
float * BW_RESTRICT s1_0,
float * s2_0,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_channels) {
BW_ASSERT(x_0 != BW_NULL);
BW_ASSERT_DEEP(bw_has_only_finite(x_0, n_channels));
BW_ASSERT(s1_0 == BW_NULL || x_0 != s1_0);
BW_ASSERT(y_0 == BW_NULL || s1_0 == BW_NULL || y_0 != s1_0);
BW_ASSERT(s2_0 == BW_NULL || x_0 != s2_0);
BW_ASSERT(y_0 == BW_NULL || s2_0 == BW_NULL || y_0 != s2_0);
BW_ASSERT(s1_0 == BW_NULL || s2_0 == BW_NULL || s1_0 != s2_0);
bw_iir2_assert_valid_coeffs(b0, b1, b2, a1, a2);
if (y_0 != BW_NULL) {
if (s1_0 != BW_NULL) {
if (s2_0 != BW_NULL)
for (size_t i = 0; i < n_channels; i++)
bw_iir2_reset(x_0[i], y_0 + i, s1_0 + i, s2_0 + i, b0, b1, b2, a1, a2);
else
for (size_t i = 0; i < n_channels; i++) {
float v_s2;
bw_iir2_reset(x_0[i], y_0 + i, s1_0 + i, &v_s2, b0, b1, b2, a1, a2);
}
} else {
if (s2_0 != BW_NULL)
for (size_t i = 0; i < n_channels; i++) {
float v_s1;
bw_iir2_reset(x_0[i], y_0 + i, &v_s1, s2_0 + i, b0, b1, b2, a1, a2);
}
else
for (size_t i = 0; i < n_channels; i++) {
float v_s1, v_s2;
bw_iir2_reset(x_0[i], y_0 + i, &v_s1, &v_s2, b0, b1, b2, a1, a2);
}
}
} else {
if (s1_0 != BW_NULL) {
if (s2_0 != BW_NULL)
for (size_t i = 0; i < n_channels; i++) {
float v_y;
bw_iir2_reset(x_0[i], &v_y, s1_0 + i, s2_0 + i, b0, b1, b2, a1, a2);
}
else
for (size_t i = 0; i < n_channels; i++) {
float v_y, v_s2;
bw_iir2_reset(x_0[i], &v_y, s1_0 + i, &v_s2, b0, b1, b2, a1, a2);
}
} else {
if (s2_0 != BW_NULL)
for (size_t i = 0; i < n_channels; i++) {
float v_y, v_s1;
bw_iir2_reset(x_0[i], &v_y, &v_s1, s2_0 + i, b0, b1, b2, a1, a2);
}
else
{} // no need to do anything
}
}
BW_ASSERT_DEEP(y_0 != BW_NULL ? bw_has_only_finite(y_0, n_channels) : 1);
BW_ASSERT_DEEP(s1_0 != BW_NULL ? bw_has_only_finite(s1_0, n_channels) : 1);
BW_ASSERT_DEEP(s2_0 != BW_NULL ? bw_has_only_finite(s2_0, n_channels) : 1);
}
static inline void bw_iir2_process1(
float x,
float * BW_RESTRICT y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2) {
BW_ASSERT(bw_is_finite(x));
BW_ASSERT(y != BW_NULL);
BW_ASSERT(s1 != BW_NULL);
BW_ASSERT(s2 != BW_NULL);
BW_ASSERT(y != s1);
BW_ASSERT(y != s2);
BW_ASSERT(s1 != s2);
BW_ASSERT(bw_is_finite(*s1));
BW_ASSERT(bw_is_finite(*s2));
bw_iir2_assert_valid_coeffs(b0, b1, b2, a1, a2);
*y = b0 * x + *s1;
*s1 = b1 * x - a1 * *y + *s2;
*s2 = b2 * x - a2 * *y;
BW_ASSERT(bw_is_finite(*y));
BW_ASSERT(bw_is_finite(*s1));
BW_ASSERT(bw_is_finite(*s2));
}
static inline void bw_iir2_process(
const float * x,
float * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_samples) {
BW_ASSERT(x != BW_NULL);
BW_ASSERT_DEEP(bw_has_only_finite(x, n_samples));
BW_ASSERT(y != BW_NULL);
BW_ASSERT(s1 != BW_NULL);
BW_ASSERT(s2 != BW_NULL);
BW_ASSERT(x != s1);
BW_ASSERT(y != s1);
BW_ASSERT(x != s2);
BW_ASSERT(y != s2);
BW_ASSERT(s1 != s2);
BW_ASSERT(bw_is_finite(*s1));
BW_ASSERT(bw_is_finite(*s2));
bw_iir2_assert_valid_coeffs(b0, b1, b2, a1, a2);
for (size_t i = 0; i < n_samples; i++)
bw_iir2_process1(x[i], y + i, s1, s2, b0, b1, b2, a1, a2);
BW_ASSERT_DEEP(bw_has_only_finite(y, n_samples));
BW_ASSERT(bw_is_finite(*s1));
BW_ASSERT(bw_is_finite(*s2));
}
static inline void bw_iir2_process_multi(
const float * const * x,
float * const * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t n_channels,
size_t n_samples) {
BW_ASSERT(x != BW_NULL);
BW_ASSERT(y != BW_NULL);
BW_ASSERT(s1 != BW_NULL);
BW_ASSERT(s2 != BW_NULL);
BW_ASSERT(s1 != s2);
#ifndef BW_NO_DEBUG
for (size_t i = 0; i < n_channels; i++) {
BW_ASSERT(x[i] != BW_NULL);
BW_ASSERT_DEEP(bw_has_only_finite(x[i], n_samples));
BW_ASSERT(y[i] != BW_NULL);
}
for (size_t i = 0; i < n_channels; i++)
for (size_t j = i + 1; j < n_channels; j++)
BW_ASSERT(y[i] != y[j]);
for (size_t i = 0; i < n_channels; i++)
for (size_t j = 0; j < n_channels; j++)
BW_ASSERT(i == j || x[i] != y[j]);
for (size_t i = 0; i < n_channels; i++) {
BW_ASSERT(bw_is_finite(s1[i]));
BW_ASSERT(bw_is_finite(s2[i]));
}
#endif
bw_iir2_assert_valid_coeffs(b0, b1, b2, a1, a2);
for (size_t j = 0; j < n_channels; j++)
for (size_t i = 0; i < n_samples; i++)
bw_iir2_process1(x[j][i], y[j] + i, s1 + j, s2 + j, b0, b1, b2, a1, a2);
#ifndef BW_NO_DEBUG
for (size_t i = 0; i < n_channels; i++) {
BW_ASSERT_DEEP(bw_has_only_finite(y[i], n_samples));
BW_ASSERT(bw_is_finite(s1[i]));
BW_ASSERT(bw_is_finite(s2[i]));
}
#endif
}
#define BW_IIR2_COEFFS_COMMON \
prewarp_freq = prewarp_at_cutoff ? cutoff : prewarp_freq; \
prewarp_freq = bw_minf(prewarp_freq, 0.499f * sample_rate); \
const float t = bw_tanf(3.141592653589793f * prewarp_freq * bw_rcpf(sample_rate)); \
const float k1 = prewarp_freq * prewarp_freq; \
const float k2 = t * cutoff; \
const float k3 = k2 * k2; \
const float k4 = k2 * prewarp_freq; \
const float k5 = Q * (k1 + k3); \
const float d = bw_rcpf(k5 + k4); \
*a1 = d * (Q + Q) * (k3 - k1); \
*a2 = d * (k5 - k4);
static inline void bw_iir2_assert_valid_params(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq) {
#ifndef BW_NO_DEBUG
BW_ASSERT(bw_is_finite(sample_rate));
BW_ASSERT(sample_rate > 0.f);
BW_ASSERT(bw_is_finite(cutoff));
BW_ASSERT(cutoff >= 1e-6f && cutoff <= 1e12f);
BW_ASSERT(bw_is_finite(Q));
BW_ASSERT(Q >= 1e-6f && Q <= 1e6f);
BW_ASSERT(prewarp_at_cutoff ? bw_is_finite(prewarp_freq) : 1);
BW_ASSERT(prewarp_at_cutoff ? prewarp_freq >= 1e-6f && prewarp_freq <= 1e12f : 1);
#else
(void)sample_rate;
(void)cutoff;
(void)Q;
(void)prewarp_at_cutoff;
(void)prewarp_freq;
#endif
}
#define BW_IIR2_ASSERT_VALID_COEFF_PTRS \
BW_ASSERT(b0 != BW_NULL); \
BW_ASSERT(b1 != BW_NULL); \
BW_ASSERT(b2 != BW_NULL); \
BW_ASSERT(a1 != BW_NULL); \
BW_ASSERT(a2 != BW_NULL); \
BW_ASSERT(b0 != b1); \
BW_ASSERT(b0 != b2); \
BW_ASSERT(b1 != b2); \
BW_ASSERT(b0 != a1); \
BW_ASSERT(b1 != a1); \
BW_ASSERT(b2 != a1); \
BW_ASSERT(b0 != a2); \
BW_ASSERT(b1 != a2); \
BW_ASSERT(b2 != a2); \
BW_ASSERT(a1 != a2);
static inline void bw_iir2_coeffs_ap2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
*b0 = *a2;
*b1 = *a1;
*b2 = 1.f;
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_bp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
*b0 = Q * k4;
*b1 = 0.f;
*b2 = -*b0;
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_hp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
*b0 = Q * k1;
*b1 = -(*b0 + *b0);
*b2 = *b0;
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_hs2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
char high_gain_dB,
float high_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_ASSERT(bw_is_finite(high_gain));
BW_ASSERT(high_gain_dB ? high_gain >= -600.f && high_gain <= 600.f : high_gain >= 1e-30f && high_gain <= 1e30f);
high_gain = high_gain_dB ? bw_dB2linf(high_gain) : high_gain;
BW_ASSERT_DEEP(cutoff * bw_sqrt(bw_sqrtf(high_gain)) >= 1e-6f && cutoff * bw_sqrt(bw_sqrtf(high_gain)) <= 1e12f);
const float sg = bw_sqrtf(high_gain);
const float ssg = bw_sqrtf(sg);
cutoff = cutoff * ssg;
BW_IIR2_COEFFS_COMMON
const float k6 = k1 * high_gain;
const float k7 = k3 - k3 * sg;
const float k8 = Q * (k7 + k6);
const float k9 = k4 * sg;
*b0 = d * (k8 + k9);
*b1 = d * (Q + Q) * (k7 - k6);
*b2 = d * (k8 - k9);
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_lp2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
*b0 = Q * k3;
*b1 = *b0 + *b0;
*b2 = *b0;
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_ls2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
char dc_gain_dB,
float dc_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_ASSERT(bw_is_finite(dc_gain));
BW_ASSERT(dc_gain_dB ? dc_gain >= -600.f && dc_gain <= 600.f : dc_gain >= 1e-30f && dc_gain <= 1e30f);
dc_gain = dc_gain_dB ? bw_dB2linf(dc_gain) : dc_gain;
BW_ASSERT_DEEP(cutoff * bw_rcpf(bw_sqrt(bw_sqrtf(dc_gain))) >= 1e-6f && cutoff * bw_rcpf(bw_sqrt(bw_sqrtf(dc_gain))) <= 1e12f);
const float sg = bw_sqrtf(dc_gain);
const float issg = bw_rcpf(bw_sqrtf(sg));
cutoff = cutoff * issg;
BW_IIR2_COEFFS_COMMON
const float k6 = k3 * (dc_gain - sg);
const float k7 = Q * (k6 + k1);
const float k8 = k4 * sg;
*b0 = d * (k7 + k8);
*b1 = d * (Q + Q) * (k6 - k1);
*b2 = d * (k7 - k8);
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_mm2(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float coeff_x,
float coeff_lp,
float coeff_bp,
float coeff_hp,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
const float k6 = k3 * (coeff_lp + coeff_x);
const float k7 = k1 * (coeff_hp + coeff_x);
const float k8 = k4 * (Q * coeff_bp + coeff_x);
const float k9 = Q * (k6 + k7);
*b0 = d * (k9 + k8);
*b1 = d * (Q + Q) * (k6 - k7);
*b2 = d * (k9 - k8);
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_notch(
float sample_rate,
float cutoff,
float Q,
char prewarp_at_cutoff,
float prewarp_freq,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
*b0 = d * k5;
*b1 = *a1;
*b2 = *b0;
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
static inline void bw_iir2_coeffs_peak(
float sample_rate,
float cutoff,
char use_bandwidth,
float Q_bandwidth,
char prewarp_at_cutoff,
float prewarp_freq,
char peak_gain_dB,
float peak_gain,
float * BW_RESTRICT b0,
float * BW_RESTRICT b1,
float * BW_RESTRICT b2,
float * BW_RESTRICT a1,
float * BW_RESTRICT a2) {
BW_ASSERT(bw_is_finite(Q_bandwidth));
BW_ASSERT(use_bandwidth ? Q_bandwidth >= 1e-6f && Q_bandwidth <= 90.f : 1);
BW_ASSERT(bw_is_finite(peak_gain));
BW_ASSERT(peak_gain_dB ? peak_gain >= -600.f && peak_gain <= 600.f : peak_gain >= 1e-30f && peak_gain <= 1e30f);
peak_gain = peak_gain_dB ? bw_dB2linf(peak_gain) : peak_gain;
float Q;
if (use_bandwidth) {
const float k6 = bw_pow2f(Q_bandwidth);
Q = bw_sqrtf(k6 * peak_gain) * bw_rcpf(k6 - 1.f);
} else
Q = Q_bandwidth;
bw_iir2_assert_valid_params(sample_rate, cutoff, Q, prewarp_at_cutoff, prewarp_freq);
BW_IIR2_ASSERT_VALID_COEFF_PTRS
BW_IIR2_COEFFS_COMMON
const float k6 = Q * (k1 + k3);
const float k7 = k4 * peak_gain;
*b0 = d * (k6 + k7);
*b1 = *a1;
*b2 = d * (k6 - k7);
bw_iir2_assert_valid_coeffs(*b0, *b1, *b2, *a1, *a2);
}
#undef BW_IIR2_COEFFS_COMMON
#if !defined(BW_CXX_NO_EXTERN_C) && defined(__cplusplus)
}
#endif
#if !defined(BW_NO_CXX) && defined(__cplusplus)
# ifndef BW_CXX_NO_ARRAY
# include <array>
# endif
namespace Brickworks {
/*** Public C++ API ***/
/*! api_cpp {{{
* ##### Brickworks::iir2Reset
* ```>>> */
template<size_t N_CHANNELS>
void iir2Reset(
const float * x0,
float * y0,
float * BW_RESTRICT s10,
float * BW_RESTRICT s20,
float b0,
float b1,
float b2,
float a1,
float a2);
# ifndef BW_CXX_NO_ARRAY
template<size_t N_CHANNELS>
void iir2Reset(
std::array<float, N_CHANNELS> x0,
std::array<float, N_CHANNELS> * BW_RESTRICT y0,
std::array<float, N_CHANNELS> * BW_RESTRICT s10,
std::array<float, N_CHANNELS> * BW_RESTRICT s20,
float b0,
float b1,
float b2,
float a1,
float a2);
# endif
template<size_t N_CHANNELS>
void iir2Process(
const float * const * x,
float * const * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t nSamples);
# ifndef BW_CXX_NO_ARRAY
template<size_t N_CHANNELS>
void iir2Process(
std::array<const float *, N_CHANNELS> x,
std::array<float *, N_CHANNELS> y,
std::array<float, N_CHANNELS> * BW_RESTRICT s1,
std::array<float, N_CHANNELS> * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t nSamples);
# endif
/*! <<<```
* }}} */
/*** Implementation ***/
/* WARNING: This part of the file is not part of the public API. Its content may
* change at any time in future versions. Please, do not use it directly. */
template<size_t N_CHANNELS>
inline void iir2Reset(
const float * x0,
float * y0,
float * BW_RESTRICT s10,
float * BW_RESTRICT s20,
float b0,
float b1,
float b2,
float a1,
float a2) {
bw_iir2_reset_multi(x0, y0, s10, s20, b0, b1, b2, a1, a2, N_CHANNELS);
}
# ifndef BW_CXX_NO_ARRAY
template<size_t N_CHANNELS>
inline void iir2Reset(
std::array<float, N_CHANNELS> x0,
std::array<float, N_CHANNELS> * BW_RESTRICT y0,
std::array<float, N_CHANNELS> * BW_RESTRICT s10,
std::array<float, N_CHANNELS> * BW_RESTRICT s20,
float b0,
float b1,
float b2,
float a1,
float a2) {
iir2Reset<N_CHANNELS>(x0.data(), y0 != BW_NULL ? y0.data() : BW_NULL, s10 != BW_NULL ? s10.data() : BW_NULL, s20 != BW_NULL ? s20.data() : BW_NULL, b0, b1, b2, a1, a2);
}
# endif
template<size_t N_CHANNELS>
inline void iir2Process(
const float * const * x,
float * const * y,
float * BW_RESTRICT s1,
float * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t nSamples) {
bw_iir2_process_multi(x, y, s1, s2, b0, b1, b2, a1, a2, N_CHANNELS, nSamples);
}
# ifndef BW_CXX_NO_ARRAY
template<size_t N_CHANNELS>
inline void iir2Process(
std::array<const float *, N_CHANNELS> x,
std::array<float *, N_CHANNELS> y,
std::array<float, N_CHANNELS> * BW_RESTRICT s1,
std::array<float, N_CHANNELS> * BW_RESTRICT s2,
float b0,
float b1,
float b2,
float a1,
float a2,
size_t nSamples) {
iir2Process<N_CHANNELS>(x.data(), y.data(), s1.data(), s2.data(), b0, b1, b2, a1, a2, nSamples);
}
# endif
}
#endif
#endif
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