One input or output transformer: band-limit, mild saturation, DC-blocked. More...

#include <diode_bridge_compressor.hpp>

Public Member Functions
void	prepare (double sample_rate)
void	reset ()
void	set_character (double character01)
	0..1 colour depth, shared with the bridge.
void	set_adaa (bool on)
double	saturate (double u) const
	u − (a/2)·u·\|u\| − (a·ε/2)·u².
double	saturate_antiderivative (double u) const
	∫sat du.
SampleType	process (SampleType input)

Static Public Attributes
static constexpr double	kLowCornerHz = 20.0
	Low-frequency corner: the transformer's LF droop, and the stage's DC block.
static constexpr double	kHighCornerHz = 28000.0
	High-frequency corner: winding bandwidth.
static constexpr double	kSaturationDepth = 0.15
	Saturation depth at character = 1.
static constexpr double	kEvenAsymmetry = 0.5
	How much of the saturation is asymmetric, i.e.
static constexpr double	kMonotonicMargin = 0.98
	Fraction of the 1/(a(1+ε)) monotonicity limit the input clamp uses.
static constexpr double	kAdaaEpsilon = 1e-5
	ADAA ill-conditioning guard, as DiodeBridgeGainT::kAdaaEpsilon.
static constexpr double	kPeakGain = 1.0
	The peak gain this stage can present, at any frequency and any amplitude.

Detailed Description

template<typename SampleType = float>
class pulp::signal::TransformerBracketT< SampleType >

One input or output transformer: band-limit, mild saturation, DC-blocked.

Peak gain is exactly 1.0, and that is load-bearing — it is the Tpeak the compressor's worst-case-gain bound multiplies by, so it has to be a property of the construction rather than a measured approximation. Three stages, each with magnitude ≤ 1 at every frequency and amplitude: a one-pole high-pass, a compressive saturator whose gain is 1 − (a/2)|u| (≤ 1 by inspection, = 1 only at the origin), and a one-pole low-pass.

Why not DcBlocker. The spec composes DcBlocker for the LF corner. Its transfer function (1 − z⁻¹)/(1 − p·z⁻¹) has magnitude 2/(1 + p) at Nyquist — 1.0025 at the default pole. Two brackets would therefore have a peak gain of 1.005, and the Tpeak = 1.0 the worst-case bound cites would be false by construction. The house TPT one-pole's high-pass output is 1 − LP, whose magnitude is ≤ 1 everywhere with equality only at Nyquist, and it is still an exact DC block (H(0) = 0). Same existing primitive family, one that does not void the invariant it is used inside.

Order: saturate, then high-pass. The saturator's even-harmonic term rectifies, so it generates a program-dependent DC offset. Placing the high-pass after it makes one filter do both jobs the spec names — the documented LF droop AND the DC block — and keeps that offset out of the output sum and out of the feedback detector, which would otherwise read it as signal and hold gain down on a silent passage.

The even harmonics are real, and they need an asymmetry to exist. The spec prescribes sat(u) = u − (a/2)·u·|u| and describes it as adding a second harmonic. It does not: u·|u| is an ODD function, so that shaper is odd-symmetric and produces odd harmonics only — which is also the physically right answer for a SYMMETRIC magnetic core. Even harmonics in a transformer come from asymmetry. kEvenAsymmetry is the parameter that supplies it, and at kEvenAsymmetry = 0 this reduces to the spec's formula exactly:

sat(u) = u − (a/2)·u·|u| − (a·ε/2)·u² slope(0) = 1

F1(u) = u²/2 − (a/6)·u²·|u| − (a·ε/6)·u³

pulp::signal::FormantVowel::a

@ a

Definition formant_filter_bank.hpp:20

pulp::signal::FormantVowel::u

@ u

Definition formant_filter_bank.hpp:20

RT contract: as the file doc block. Nothing allocates.