pulp::signal::SaturatorAdaa2 Class Reference

Second-order antiderivative antialiasing over one shape, in the curve's own argument domain (Bilbao, Esqueda, Parker & Välimäki, IEEE SPL 24(7), 2017). More...

#include <saturator.hpp>

Public Member Functions
void	reset (SaturatorShape shape, double previous, double before)
	Seeds the two-sample history: previous is the last argument consumed, before the one ahead of it.
double	step (SaturatorShape shape, double u)
	Consumes the newest argument and returns the antialiased curve value centred one sample back.

Static Public Attributes
static constexpr double	kTolerance = 1e-4
	Relative spacing below which a divided difference is replaced by its series limit.

Detailed Description

Second-order antiderivative antialiasing over one shape, in the curve's own argument domain (Bilbao, Esqueda, Parker & Välimäki, IEEE SPL 24(7), 2017).

The output is twice the second divided difference of F2 over the last three arguments; on the linear part of a curve that is the mean of the three samples. Because a divided difference is symmetric in its points, the three arguments are taken in sorted order: the denominator is then the full spread of the three, never the gap between two points that happen to be close, which is what makes a signal turning around (x[n] ≈ x[n−2]) a non-event rather than the ill-conditioned special case it is in the textbook arrangement.

Near-degenerate spacings fall back to series forms that are accurate to the order the fallback threshold leaves: a close pair uses the midpoint rule with its second-order correction, a near-constant triple uses the curve at the triple's mean (the limit of the divided difference, and exact on the linear part). The threshold scales with |u| because F2 grows as u², so the rounding error the division amplifies stays bounded (~1e-8 absolute) at every drive.

The three-point stencil is symmetric about the middle sample, so the output is delayed by exactly one sample. Scalar state only; step() never allocates.

Member Function Documentation

reset()

void pulp::signal::SaturatorAdaa2::reset ( SaturatorShape shape, double previous, double before )

inline

Seeds the two-sample history: previous is the last argument consumed, before the one ahead of it.

A parameter change that remaps the argument domain re-seeds from the same input history, so the stencil never mixes arguments taken under two different settings.

step()

double pulp::signal::SaturatorAdaa2::step ( SaturatorShape shape, double u )

inline

Consumes the newest argument and returns the antialiased curve value centred one sample back.

Member Data Documentation

kTolerance

double pulp::signal::SaturatorAdaa2::kTolerance = 1e-4

staticconstexpr

Relative spacing below which a divided difference is replaced by its series limit.

[design parameter] default 1e-4, range 1e-6 .. 1e-3.

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The documentation for this class was generated from the following file:

• /home/runner/work/pulp/pulp/core/signal/include/pulp/signal/saturator.hpp