class
SushiDSP::Biquad
Direct Form I biquad filter with RBJ cookbook coefficient derivation, its coefficients and state in double behind a float sample interface (docs/archive/superpowers/specs/2026-09-07-grid-knee-antialiasing-design.md section 15).
- Declared in
include/SushiDSP/math/Biquad.hpp
Public member functions
void set_low_pass(double sample_rate, double cutoff_hz, double q)Configures this filter as a low-pass with the given cutoff and Q.
Parameters
sample_rateSample rate in Hz.
cutoff_hzCutoff frequency in Hz.
qQuality factor (0.707 = Butterworth).
void set_one_pole_low_pass(double sample_rate, double cutoff_hz)Configures this filter as a first-order (one-pole) low-pass.
A single RC section, bilinear-transformed with the corner prewarped, so the second numerator and denominator taps are zero. This is the right shape for a physical RC pole - a Butterworth biquad would roll off at twice the rate a real one does.
Parameters
sample_rateSample rate in Hz.
cutoff_hzCorner frequency in Hz, where the response is -3 dB.
void set_first_order_high_pass(double sample_rate, double cutoff_hz)Configures this filter as a first-order (one-pole) high-pass.
A single RC section mapped by the impulse-invariant pole R = exp(-2*pi*fc/fs): unity at Nyquist and -3 dB at the corner (include/SushiDSP/README.md).
Parameters
cutoff_hzCorner frequency in Hz, where the response is -3 dB.
Precondition
0 < cutoff_hz < sample_rate / 2
void set_high_pass(double sample_rate, double cutoff_hz, double q)Configures this filter as a high-pass with the given cutoff and Q.
Parameters
sample_rateSample rate in Hz.
cutoff_hzCutoff frequency in Hz.
qQuality factor (0.707 = Butterworth).
Precondition
cutoff_hz / sample_rate >= 1e-4; use set_first_order_high_pass for corners that low.
void set_low_shelf(double sample_rate, double cutoff_hz, double gain_db, double q)Configures this filter as a low-shelf with the given corner, gain, and Q.
Parameters
sample_rateSample rate in Hz.
cutoff_hzShelf corner frequency in Hz.
gain_dbShelf gain in decibels (positive boosts, negative cuts).
qShelf slope parameter (RBJ cookbook S=1 equivalent at q=1.0).
void set_high_shelf(double sample_rate, double cutoff_hz, double gain_db, double q)Configures this filter as a high-shelf with the given corner, gain, and Q.
Parameters
sample_rateSample rate in Hz.
cutoff_hzShelf corner frequency in Hz.
gain_dbShelf gain in decibels.
qShelf slope parameter.
void set_peaking(double sample_rate, double center_hz, double gain_db, double q)Configures this filter as a peaking EQ with the given center, gain, and Q.
Parameters
sample_rateSample rate in Hz.
center_hzCenter frequency in Hz.
gain_dbPeak gain in decibels (positive boosts, negative cuts).
qBandwidth parameter (higher Q = narrower peak).
void set_first_order_shelf(double sample_rate, double zero_hz, double pole_hz, double low_frequency_gain)Configures this filter as a first-order shelf with independent zero and pole.
Both corners are prewarped separately, so a mirrored pair cancels exactly; see docs/archive/superpowers/specs/2026-09-05-dd3-spx90-design.md for the derivation.
Parameters
sample_rateSample rate in Hz.
zero_hzFrequency of the transfer function's zero, in Hz.
pole_hzFrequency of its pole, in Hz.
low_frequency_gainGain below both corners; 1.0 is unity.
float process_sample(float input)Processes one sample through the filter.
Parameters
inputThe input sample.
Returns
The filtered output sample.
void reset()Clears the filter's internal state.
void set_coefficients(double b0, double b1, double b2, double a1, double a2)Loads five coefficients computed elsewhere, leaving the state untouched.
Parameters
b0Feed-forward tap on the current input, already divided by a0.
b1Feed-forward tap on the previous input, already divided by a0.
b2Feed-forward tap on the input before that, already divided by a0.
a1Feedback tap on the previous output, already divided by a0.
a2Feedback tap on the output before that, already divided by a0.
Precondition
|a2| < 1 and |a1| < 1 + a2, so the poles lie inside the unit circle.