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#ifndef FILTERS_BIQUAD_H
#define FILTERS_BIQUAD_H
#include <cmath>
#include <cstddef>
#include <utility>
#include "math_defs.h"
/* Filters implementation is based on the "Cookbook formulae for audio
* EQ biquad filter coefficients" by Robert Bristow-Johnson
* http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
*/
/* Implementation note: For the shelf and peaking filters, the specified gain
* is for the centerpoint of the transition band. This better fits EFX filter
* behavior, which expects the shelf's reference frequency to reach the given
* gain. To set the gain for the shelf or peak itself, use the square root of
* the desired linear gain (or halve the dB gain).
*/
enum class BiquadType {
/** EFX-style low-pass filter, specifying a gain and reference frequency. */
HighShelf,
/** EFX-style high-pass filter, specifying a gain and reference frequency. */
LowShelf,
/** Peaking filter, specifying a gain and reference frequency. */
Peaking,
/** Low-pass cut-off filter, specifying a cut-off frequency. */
LowPass,
/** High-pass cut-off filter, specifying a cut-off frequency. */
HighPass,
/** Band-pass filter, specifying a center frequency. */
BandPass,
};
template<typename Real>
class BiquadFilterR {
/* Last two delayed components for direct form II. */
Real z1{0.0f}, z2{0.0f};
/* Transfer function coefficients "b" (numerator) */
Real b0{1.0f}, b1{0.0f}, b2{0.0f};
/* Transfer function coefficients "a" (denominator; a0 is pre-applied). */
Real a1{0.0f}, a2{0.0f};
public:
void clear() noexcept { z1 = z2 = 0.0f; }
/**
* Sets the filter state for the specified filter type and its parameters.
*
* \param type The type of filter to apply.
* \param gain The gain for the reference frequency response. Only used by
* the Shelf and Peaking filter types.
* \param f0norm The reference frequency normal (ref_freq / sample_rate).
* This is the center point for the Shelf, Peaking, and
* BandPass filter types, or the cutoff frequency for the
* LowPass and HighPass filter types.
* \param rcpQ The reciprocal of the Q coefficient for the filter's
* transition band. Can be generated from rcpQFromSlope or
* rcpQFromBandwidth as needed.
*/
void setParams(BiquadType type, Real gain, Real f0norm, Real rcpQ);
void copyParamsFrom(const BiquadFilterR &other)
{
b0 = other.b0;
b1 = other.b1;
b2 = other.b2;
a1 = other.a1;
a2 = other.a2;
}
void process(Real *dst, const Real *src, const size_t numsamples);
/* Rather hacky. It's just here to support "manual" processing. */
std::pair<Real,Real> getComponents() const noexcept
{ return {z1, z2}; }
void setComponents(Real z1_, Real z2_) noexcept
{ z1 = z1_; z2 = z2_; }
Real processOne(const Real in, Real &z1_, Real &z2_) const noexcept
{
Real out{in*b0 + z1_};
z1_ = in*b1 - out*a1 + z2_;
z2_ = in*b2 - out*a2;
return out;
}
/**
* Calculates the rcpQ (i.e. 1/Q) coefficient for shelving filters, using
* the reference gain and shelf slope parameter.
* \param gain 0 < gain
* \param slope 0 < slope <= 1
*/
static Real rcpQFromSlope(Real gain, Real slope)
{ return std::sqrt((gain + 1.0f/gain)*(1.0f/slope - 1.0f) + 2.0f); }
/**
* Calculates the rcpQ (i.e. 1/Q) coefficient for filters, using the
* normalized reference frequency and bandwidth.
* \param f0norm 0 < f0norm < 0.5.
* \param bandwidth 0 < bandwidth
*/
static Real rcpQFromBandwidth(Real f0norm, Real bandwidth)
{
const Real w0{al::MathDefs<Real>::Tau() * f0norm};
return 2.0f*std::sinh(std::log(Real{2.0f})/2.0f*bandwidth*w0/std::sin(w0));
}
};
using BiquadFilter = BiquadFilterR<float>;
#endif /* FILTERS_BIQUAD_H */
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