fourier.h File Reference

Bandlimited Fourier waveform kernels (BLIT / PolyBLEP / miniBLEP). More...

#include <complex.h>
#include <stdbool.h>
#include <stddef.h>
#include <stdint.h>
#include "oakfield/field.h"

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Classes
struct	SimComplexDouble
	Explicit in-memory representation for a complex double scalar (re, im) More...

Macros
#define	SIM_FOURIER_ASSUME_VALID   0
	Skip hot-path argument clamps when inputs are validated by caller.
#define	SIM_FOURIER_MINIBLEP_SPAN   4.0
	Two-sided BLIT support window (in units of phase increment): wider -> cleaner stopband.
#define	SIM_FOURIER_MINIBLEP_MAX_WINDOW   0.5
	Maximum miniBLEP window in normalized phase (0..1).
#define	SIM_FOURIER_INTEGRATOR_LEAK   1e-9
	Small leak to keep BLIT integrators numerically bounded.

Typedefs
typedef struct SimComplexDouble	SimComplexDouble
	Fallback ABI-compatible complex double if not defined in field.h.

Functions
double	sim_fourier_dirichlet (double phase_radians, int harmonic_count)
	Normalized Dirichlet kernel D_M(φ) = sin(Mφ/2)/(M sin(φ/2)).
SimComplexDouble	sim_fourier_dirichlet_complex (SimComplexDouble phase_radians, int harmonic_count)
	Complex Dirichlet kernel.
double	sim_fourier_blit (double phase_radians, int harmonic_count)
	DC-corrected BLIT for saw/triangle integration: D_M(φ) − 1/M.
SimComplexDouble	sim_fourier_blit_complex (SimComplexDouble phase_radians, int harmonic_count)
	Complex BLIT (DC-corrected).
double	sim_fourier_saw_blit (double phase_radians, double phase_increment_radians, int harmonic_count, double *state)
	Bandlimited saw from BLIT integration.
SimComplexDouble	sim_fourier_saw_blit_complex (SimComplexDouble phase_radians, double phase_increment_radians, int harmonic_count, SimComplexDouble *state)
	Complex BLIT saw (integrates complex BLIT).
double	sim_fourier_square_blit (double phase_radians, double phase_increment_radians, int harmonic_count, double duty, double *state)
	Bandlimited square via phase-shifted BLIT difference and integration.
SimComplexDouble	sim_fourier_square_blit_complex (SimComplexDouble phase_radians, double phase_increment_radians, int harmonic_count, double duty, SimComplexDouble *state)
	Complex BLIT square.
double	sim_fourier_triangle_blit (double phase_radians, double phase_increment_radians, int harmonic_count, double *velocity_state, double *position_state)
	Triangle from double-integrated BLIT square (velocity + position states).
SimComplexDouble	sim_fourier_triangle_blit_complex (SimComplexDouble phase_radians, double phase_increment_radians, int harmonic_count, SimComplexDouble *velocity_state, SimComplexDouble *position_state)
	Complex BLIT triangle (double integration).
double	sim_fourier_polyblep (double phase, double dphase)
	Two-point PolyBLEP step correction (subtract from naive saw/square).
SimComplexDouble	sim_fourier_polyblep_complex (double phase, double dphase)
	Complex PolyBLEP (imaginary part = 0).
double	sim_fourier_polyblamp (double phase, double dphase)
	PolyBLAMP (integral of PolyBLEP) for slope/kink smoothing.
SimComplexDouble	sim_fourier_polyblamp_complex (double phase, double dphase)
	Complex PolyBLAMP.
double	sim_fourier_miniblep (double phase, double dphase)
	Table-driven miniBLEP (windowed-sinc step) for high stopband rejection.
SimComplexDouble	sim_fourier_miniblep_complex (double phase, double dphase)
	Complex miniBLEP.
double	sim_fourier_miniblamp (double phase, double dphase)
	miniBLAMP (integrated miniBLEP) for slope discontinuities (triangle).
SimComplexDouble	sim_fourier_miniblamp_complex (double phase, double dphase)
	Complex miniBLAMP.

Detailed Description

Bandlimited Fourier waveform kernels (BLIT / PolyBLEP / miniBLEP).

This header provides reusable kernels for research-grade saw, square, and triangle oscillators:

• BLIT (Dirichlet kernel) + integration for analytical Fourier-series control.
• PolyBLEP / PolyBLAMP for real-time anti-aliased steps and slope changes.
• miniBLEP / miniBLAMP (windowed-sinc table) for higher-stopband rejection.

All routines use double precision. Complex variants use SimComplexDouble for ABI stability and mirror the real APIs.

Macro Definition Documentation

SIM_FOURIER_ASSUME_VALID

#define SIM_FOURIER_ASSUME_VALID   0

Skip hot-path argument clamps when inputs are validated by caller.

0 = clamp/guard (default), 1 = assume phase/duty in-range; debug builds assert.

SIM_FOURIER_MINIBLEP_SPAN

#define SIM_FOURIER_MINIBLEP_SPAN   4.0

Two-sided BLIT support window (in units of phase increment): wider -> cleaner stopband.

The miniBLEP/miniBLAMP kernels are stretched over SIM_FOURIER_MINIBLEP_SPAN phase increments but capped at SIM_FOURIER_MINIBLEP_MAX_WINDOW to avoid consuming an entire period near Nyquist.

Function Documentation

sim_fourier_dirichlet()

double sim_fourier_dirichlet	(	double	phase_radians,
		int	harmonic_count
	)

Normalized Dirichlet kernel D_M(φ) = sin(Mφ/2)/(M sin(φ/2)).

Parameters

phase_radians	Instantaneous phase in radians (wrap to 2π is optional).
harmonic_count	N = number of positive harmonics below Nyquist.

Implementation detail:

• We internally build an odd Dirichlet length M = 2N + 1 to preserve 2π periodicity.
• DC correction terms use this M (see sim_fourier_blit).

  Returns

  BLIT sample with DC gain of 1.

sim_fourier_miniblep()

double sim_fourier_miniblep	(	double	phase,
		double	dphase
	)

Table-driven miniBLEP (windowed-sinc step) for high stopband rejection.

Parameters

phase	Normalized phase in [0,1).
dphase	Normalized phase increment (f / fs).

Returns

Correction to subtract from a naive discontinuity.

sim_fourier_polyblep()

double sim_fourier_polyblep	(	double	phase,
		double	dphase
	)

Two-point PolyBLEP step correction (subtract from naive saw/square).

Parameters

phase	Normalized phase in [0,1).
dphase	Normalized phase increment per sample (f / fs).

sim_fourier_saw_blit()

double sim_fourier_saw_blit	(	double	phase_radians,
		double	phase_increment_radians,
		int	harmonic_count,
		double *	state
	)

Bandlimited saw from BLIT integration.

Parameters

	phase_radians	Phase in radians.
	phase_increment_radians	Per-sample phase advance (2π f / fs).
	harmonic_count	Number of partials (see sim_fourier_dirichlet).
[in,out]	state	Single-pole integrator state (initialize to 0).

Returns

Saw sample (approximately unity peak-to-peak).

sim_fourier_square_blit()

double sim_fourier_square_blit	(	double	phase_radians,
		double	phase_increment_radians,
		int	harmonic_count,
		double	duty,
		double *	state
	)

Bandlimited square via phase-shifted BLIT difference and integration.

Parameters

phase_radians	Current oscillator phase.
phase_increment_radians	Phase increment per output sample.
harmonic_count	Number of harmonics to include.
duty	Duty cycle in [0,1]; 0.5 yields a symmetric square.
state	Integrator state for the BLIT accumulator.

sim_fourier_triangle_blit()

double sim_fourier_triangle_blit	(	double	phase_radians,
		double	phase_increment_radians,
		int	harmonic_count,
		double *	velocity_state,
		double *	position_state
	)

Triangle from double-integrated BLIT square (velocity + position states).

Parameters

phase_radians	Current oscillator phase.
phase_increment_radians	Phase increment per output sample.
harmonic_count	Number of harmonics to include.
velocity_state	First integrator (square accumulator), init to 0.
position_state	Second integrator (triangle accumulator), init to 0.