frequency_response.hpp File Reference

Evaluate what a biquad (or a cascade of them) does to the spectrum. More...

#include <pulp/signal/biquad.hpp>
#include <algorithm>
#include <cmath>
#include <complex>
#include <cstddef>
#include <span>

Go to the source code of this file.

Namespaces
namespace	pulp
namespace	pulp::signal

Functions
float	pulp::signal::magnitude_to_db (double magnitude)
	Convert a linear magnitude to dB, floored at min_response_db.
template<typename SampleType>
double	pulp::signal::section_magnitude (const BiquadCoefficientsT< SampleType > &c, double omega)
	Linear magnitude |H(e^jω)| of one section at normalized angular frequency ω = 2π·f/fs (radians/sample, meaningful over [0, π]).
double	pulp::signal::section_magnitude (const BiquadCoefficients &c, double omega)
template<typename SampleType>
double	pulp::signal::section_group_delay (const BiquadCoefficientsT< SampleType > &c, double omega)
	Group delay of one biquad section at omega (radians per sample), in samples: -d(arg H)/d(omega) for H = B/A, evaluated in closed form as tau(B) - tau(A) with tau(P) = Re(sum k p_k z^-k / sum p_k z^-k), so no numeric differentiation is involved.
template<typename SampleType, std::size_t Extent>
double	pulp::signal::cascade_magnitude (std::span< const BiquadCoefficientsT< SampleType >, Extent > sos, double omega)
	Linear magnitude |H| of a cascade at angular frequency ω.
double	pulp::signal::cascade_magnitude (std::span< const BiquadCoefficients > sos, double omega)
double	pulp::signal::angular_frequency (double freq_hz, double sample_rate)
	Angular frequency (radians/sample) of freq_hz at sample_rate, clamped to [0, π].
template<typename SampleType>
float	pulp::signal::section_magnitude_db (const BiquadCoefficientsT< SampleType > &c, double freq_hz, double sample_rate)
	Magnitude of one section at a frequency in Hz, in dB.
float	pulp::signal::section_magnitude_db (const BiquadCoefficients &c, double freq_hz, double sample_rate)
template<typename SampleType, std::size_t Extent>
float	pulp::signal::cascade_magnitude_db (std::span< const BiquadCoefficientsT< SampleType >, Extent > sos, double freq_hz, double sample_rate)
	Magnitude of a cascade at a frequency in Hz, in dB.
float	pulp::signal::cascade_magnitude_db (std::span< const BiquadCoefficients > sos, double freq_hz, double sample_rate)
template<typename SampleType>
float	pulp::signal::magnitude_db (const BiquadT< SampleType > &filter, double freq_hz, double sample_rate)
	Ask a live filter what it looks like: the magnitude, in dB, that this BiquadT is applying at freq_hz with its coefficients as they stand.
double	pulp::signal::fft_bin_frequency (std::size_t index, std::size_t bin_count, double sample_rate)
	Center frequency of bin index in a real-FFT magnitude array.
double	pulp::signal::log_frequency_at (std::size_t index, std::size_t count, double min_hz, double max_hz)
	Frequency of sample index of count, log-spaced across [min_hz, max_hz].
template<typename SampleType, std::size_t Extent>
void	pulp::signal::response_curve_db (std::span< const BiquadCoefficientsT< SampleType >, Extent > sos, double min_hz, double max_hz, double sample_rate, std::span< float > out)
	Sample a cascade's magnitude response into out, at out.size() log-spaced frequencies spanning [min_hz, max_hz], in dB.
void	pulp::signal::response_curve_db (std::span< const BiquadCoefficients > sos, double min_hz, double max_hz, double sample_rate, std::span< float > out)

Variables
constexpr float	pulp::signal::min_response_db = -200.0f
	Floor applied to dB conversions.

Detailed Description

Evaluate what a biquad (or a cascade of them) does to the spectrum.

This is the analysis half of the biquad story. The design half (filter_design.hpp / iir_design.hpp) turns filter parameters into coefficients; BiquadT runs those coefficients over samples. Neither can answer "what curve does this filter draw?" — that is what lives here.

Every entry point takes the canonical BiquadCoefficientsT from biquad.hpp, preserving its float or double coefficient precision, so the same section that is processing audio right now (via BiquadT::coefficients()) is the one being plotted. A UI never has to re-derive, and therefore never has to approximate, a filter's shape.

RT contract: allocation-free. These are trig-heavy and meant for control-rate / UI use, not the audio callback.