biquad_low_shelf()

MAYAFLUX_API void MayaFlux::Kinesis::Discrete::biquad_low_shelf	(	double	frequency,
		double	slope,
		double	gain_db,
		double	sample_rate,
		std::vector< double > &	a,
		std::vector< double > &	b
	)

Second-order low shelf coefficients.

Parameters

frequency	Shelf midpoint in Hz
slope	Shelf slope; 1.0 is the steepest without overshoot
gain_db	Shelf level relative to unity, in dB
sample_rate	Sampling rate in Hz
a	Denominator output, resized to 3, a[0] == 1.0
b	Numerator output, resized to 3

Definition at line 138 of file Coefficients.cpp.

{
    const double amp = db_to_amplitude_sqrt(gain_db);
    const double nyquist = sample_rate * 0.5;
    const double f = std::clamp(frequency, 1.0, nyquist - 1.0);
    const double w0 = 2.0 * std::numbers::pi * f / sample_rate;
    const double cosw0 = std::cos(w0);
    const double s = std::clamp(slope, 1e-4, 1.0);
    const double alpha = std::sin(w0) * 0.5
        * std::sqrt((amp + 1.0 / amp) * (1.0 / s - 1.0) + 2.0);
    const double sq = 2.0 * std::sqrt(amp) * alpha;
 
    emit(a, b,
        (amp + 1.0) + (amp - 1.0) * cosw0 + sq,
        -2.0 * ((amp - 1.0) + (amp + 1.0) * cosw0),
        (amp + 1.0) + (amp - 1.0) * cosw0 - sq,
        amp * ((amp + 1.0) - (amp - 1.0) * cosw0 + sq),
        2.0 * amp * ((amp - 1.0) - (amp + 1.0) * cosw0),
        amp * ((amp + 1.0) - (amp - 1.0) * cosw0 - sq));
}

References a, alpha, b, cosw0, frequency, and w0.