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+#ifndef FILTERS_BIQUAD_H
+#define FILTERS_BIQUAD_H
+
+#include <cmath>
+#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 filters, the specified gain is for the
+ * reference frequency, which is the centerpoint of the transition band. This
+ * better matches EFX filter design. To set the gain for the shelf 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, int 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 */