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Implement "vicanek" matched biquad filters

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This commit is contained in:
Robin Gareus 2022-10-31 20:49:42 +01:00
parent 6e3d3706dc
commit 5599e136c0
Signed by: rgareus
GPG Key ID: A090BCE02CF57F04
3 changed files with 108 additions and 1 deletions
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9
libs/ardour/ardour/dsp_filter.h
View File

@ -220,7 +220,11 @@ namespace ARDOUR { namespace DSP {
AllPass,
Peaking,
LowShelf,
HighShelf
HighShelf,
MatchedLowPass,
MatchedHighPass,
MatchedBandPass0dB,
MatchedPeaking
};
/** Instantiate Biquad Filter
@ -260,6 +264,9 @@ namespace ARDOUR { namespace DSP {
/** reset filter state */
void reset () { _z1 = _z2 = 0.0; }
private:
void set_vicanek_poles (const double W0, const double Q, const double A = 1.0);
void calc_vicanek (const double W0, double& A0, double& A1, double& A2, double& phi0, double& phi1, double& phi2);
double _rate;
float _z1, _z2;
double _a1, _a2;

96
libs/ardour/dsp_filter.cc
View File

@ -206,6 +206,35 @@ Biquad::configure (Biquad const& other)
_b2 = other._b2;
}
void
Biquad::set_vicanek_poles (const double W0, const double Q, const double A)
{
/* https://www.vicanek.de/articles/BiquadFits.pdf */
const double Q2 = Q * Q;
const double AA = A * A;
const double p = 1. / (4 * AA * Q2);
_a2 = exp (-.5 * W0 / (A * Q));
_a1 = p <= 1.
? -2 * _a2 * cos (W0 * sqrt (1 - p))
: -2 * _a2 * cosh (W0 * sqrt (p - 1));
_a2 = _a2 * _a2;
}
void
Biquad::calc_vicanek (const double W0, double& A0, double& A1, double& A2, double& phi0, double& phi1, double& phi2)
{
#define SQR(x) ((x) * (x))
A0 = SQR(1. + _a1 + _a2);
A1 = SQR(1. - _a1 + _a2);
A2 = -4 * _a2;
phi1 = SQR(sin (.5 * W0));
phi0 = 1.0 - phi1;
phi2 = 4 * phi0 * phi1;
#undef SQR
}
void
Biquad::compute (Type type, double freq, double Q, double gain)
{
@ -219,12 +248,15 @@ Biquad::compute (Type type, double freq, double Q, double gain)
*/
const double A = pow (10.0, (gain / 40.0));
const double W0 = (2.0 * M_PI * freq) / _rate;
const double sinW0 = sin (W0);
const double cosW0 = cos (W0);
const double alpha = sinW0 / (2.0 * Q);
const double beta = sqrt (A) / Q;
double _a0;
double A0, A1, A2;
double phi0, phi1, phi2;
switch (type) {
case LowPass:
@ -307,6 +339,70 @@ Biquad::compute (Type type, double freq, double Q, double gain)
_a1 = 2.0 * ((A - 1) - ((A + 1) * cosW0));
_a2 = (A + 1) - ((A - 1) * cosW0) - (beta * sinW0);
break;
case MatchedHighPass:
_a0 = 1.0;
set_vicanek_poles (W0, Q);
calc_vicanek (W0, A0, A1, A2, phi0, phi1, phi2);
_b0 = sqrt (A0 * phi0 + A1 * phi1 + A2 * phi2) / (4 * phi1) * Q;
_b1 = -2 * _b0;
_b2 = _b0;
break;
case MatchedLowPass:
_a0 = 1.0;
set_vicanek_poles (W0, Q);
calc_vicanek (W0, A0, A1, A2, phi0, phi1, phi2);
{
const double B0_2 = 1 + _a1 + _a2; // = sqrt (B0)
const double B1 = ((A0 * phi0 + A1 * phi1 + A2 * phi2) * Q * Q - A0 * phi0) / phi1;
_b0 = .5 * (B0_2 + sqrt (B1));
_b1 = B0_2 -_b0;
_b2 = 0;
}
break;
case MatchedBandPass0dB: /* Constant 0 dB peak gain */
_a0 = 1.0;
set_vicanek_poles (W0, Q);
{
float fq = 2 * freq / _rate;
float fq2 = fq * fq;
_b1 = -.5 * (1 - _a1 + _a2) * fq / Q / sqrt ((1 - fq2) * (1 - fq2) + fq2 / (Q * Q));
_b0 = .5 * ((1 + _a1 + _a2) / (W0 * Q) - _b1);
_b2 = -_b0 - _b1;
}
break;
case MatchedPeaking:
_a0 = 1.0;
set_vicanek_poles (W0, Q, A);
calc_vicanek (W0, A0, A1, A2, phi0, phi1, phi2);
{
const double AA = A * A;
const double AAAA = AA * AA;
const double R1 = (phi0 * A0 + phi1 * A1 + phi2 * A2) * AAAA;
const double R2 = (A1 - A0 + 4 * (phi0 - phi1) * A2) * AAAA;
const double B0 = A0;
const double B2 = (R1 - phi1 * R2 - B0) / (4 * phi1 * phi1);
const double B1 = R2 + B0 + 4 * (phi1 - phi0) * B2;
const double B0_2 = 1 + _a1 + _a2; // = sqrt (B0)
_b1 = .5 * (B0_2 - sqrt (B1));
const double w = B0_2 - _b1;
_b0 = .5 * (w + sqrt (w * w + B2));
_b2 = -B2 / (4 * _b0);
}
break;
default:
abort(); /*NOTREACHED*/
break;

4
libs/ardour/luabindings.cc
View File

@ -3082,6 +3082,10 @@ LuaBindings::common (lua_State* L)
.addConst ("Peaking", ARDOUR::DSP::Biquad::Peaking)
.addConst ("LowShelf", ARDOUR::DSP::Biquad::LowShelf)
.addConst ("HighShelf", ARDOUR::DSP::Biquad::HighShelf)
.addConst ("MatchedLowPass", ARDOUR::DSP::Biquad::MatchedLowPass)
.addConst ("MatchedHighPass", ARDOUR::DSP::Biquad::MatchedHighPass)
.addConst ("MatchedBandPass0dB", ARDOUR::DSP::Biquad::MatchedBandPass0dB)
.addConst ("MatchedPeaking", ARDOUR::DSP::Biquad::MatchedPeaking)
.endNamespace ()
.beginNamespace ("NoiseType")