Triangle Wave Oscillator
Overview
The triangle wave oscillator programmatically generates a triangle waveform that ramps up from 0.0 to 1.0, then ramps down to -1.0, and ramps back up to 0.0. The basic_triangle_osc is not bandwidth limited, while triangle_osc is, using a technique called "PolyBLAMP" to reduce aliasing artifacts that can occur when generating the triangle waveform with sharp corners.
PolyBLAMP uses the BLAMP (bandlimited ramp) function to treat any discontinuities found in the first derivative of a signal by quasi-bandlimiting the corners found in the waveform. The algorithm derives a polynomial approximation of the BLAMP function, making it efficient for implementation. This correction function is applied to the generated waveform, effectively removing frequencies above the waveform’s Nyquist frequency to avoid aliasing artifacts.
Declaration
struct basic_triangle_osc
{
constexpr float operator()(phase p) const;
constexpr float operator()(phase_iterator i) const;
};
constexpr auto basic_triangle = basic_triangle_osc{};
struct triangle_osc
{
constexpr float operator()(phase p, phase dt) const;
constexpr float operator()(phase_iterator i) const;
};
constexpr auto triangle = triangle_osc{};Expressions
basic_triangle_osc is a model of BasicOscillator and implements all valid expressions of BasicOscillator. triangle_osc is a model of BandwidthLimitedOscillator and implements all valid expressions of BandwidthLimitedOscillator.
basic_triangle_osc and triangle_osc are stateless. The global instances basic_triangle and triangle can be used anywhere without needing to be placed in a class or struct. They are semantically equivalent to global functions.