polyblep.hpp

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// sbl/dsp/polyblep.hpp — Polynomial band-limited step (Audio Stack — Atoms)
//
// PolyBLEP correction for band-limited waveform synthesis.
//
// Two function pairs:
//   this_blep / next_blep — correct step discontinuities (saw, square)
//   this_integrated_blep / next_integrated_blep — correct slope
//       discontinuities (triangle, variable-slope ramps)
//
// Adapted from Mutable Instruments stmlib/dsp/polyblep.h (MIT license).
// Copyright 2017 Emilie Gillet.
//
// Usage (step discontinuity — saw reset):
//   float t = phase_overshoot / frequency;
//   this_sample -= this_blep(t);
//   next_sample -= next_blep(t);
//
// Usage (slope discontinuity — triangle inflection):
//   float discontinuity = (slope_up + slope_down) * frequency;
//   this_sample -= this_integrated_blep(t) * discontinuity;
//   next_sample -= next_integrated_blep(t) * discontinuity;
 
#pragma once
 
namespace sbl::dsp::polyblep {
 
// --- Step BLEP (2nd-order) — for value discontinuities ---
 
/// Correction for the current sample at a step discontinuity.
/// t = normalized time since discontinuity (phase overshoot / frequency).
inline float this_blep(float t) {
    return 0.5f * t * t;
}
 
/// Correction for the next sample at a step discontinuity.
inline float next_blep(float t) {
    t = 1.0f - t;
    return -0.5f * t * t;
}
 
// --- Integrated BLEP (4th-order) — for slope discontinuities ---
 
/// Correction for the next sample at a slope discontinuity.
/// 4th-order polynomial: antiderivative of the quadratic BLEP.
/// Multiply by (slope_up + slope_down) * frequency to get the actual correction.
inline float next_integrated_blep(float t) {
    const float t1 = 0.5f * t;
    const float t2 = t1 * t1;
    const float t4 = t2 * t2;
    return 0.1875f - t1 + 1.5f * t2 - t4;
}
 
/// Correction for the current sample at a slope discontinuity.
inline float this_integrated_blep(float t) {
    return next_integrated_blep(1.0f - t);
}
 
} // namespace sbl::dsp::polyblep