minBLEP

minBLEP, short for minimum-phase band-limited step, is a technique used in digital audio synthesis to reduce aliasing caused by discontinuities in waveforms. It is a variant of the band-limited step (BLEP) method and is designed to produce cleaner transitions in digitally generated signals.

The core idea is to replace a sharp waveform edge with a short, precomputed segment whose spectrum is band-limited. The minBLEP segment uses a minimum-phase impulse response, which is causal and concentrates its energy toward the start of the transition. This minimizes phase distortion and time-domain artifacts while still suppressing high-frequency content that would alias when the edge is synthesized digitally.

In practice, a set of minBLEP waveforms of different lengths is precomputed and stored in a table. During synthesis, whenever the oscillator’s phase accumulator crosses a discontinuity (such as a phase wrap or a pulse edge), a scaled minBLEP tail is added to the output over a short window. This tail cancels the spectral components that would otherwise alias, producing a smoother, more band-limited waveform.

Advantages of minBLEP include effective alias suppression with compact transition windows and better temporal localization, making it well suited for real-time oscillator implementations. Limitations involve the need for precomputed tables and careful handling of scaling to ensure proper amplitude, particularly at high frequencies or with complex modulation.

See also: band-limited step, BLEP, polyBLEP, aliasing in digital audio, oscillator synthesis.