BLEP

BLEP, or Band-Limited Step, is a technique used in digital audio synthesis to reduce aliasing produced by abrupt waveform transitions in discrete-time oscillators. The method replaces instantaneous discontinuities in a waveform with small, precomputed, band-limited transition shapes. When a periodic waveform such as a square, sawtooth, or pulse crosses a discontinuity in the digital domain, naive sample values generate high-frequency content that exceeds the Nyquist limit, producing audible aliasing. A BLEP approach inserts a short corrective pulse around the discontinuity, drawn from a fixed, low-pass-like shape, and scaled to the size of the step. The result is a waveform whose spectrum is more faithfully band-limited to the sampling rate.

In practice, an oscillator implementation detects discontinuities in phase or value and adds the BLEP shape to a handful of subsequent samples. The effect is essentially to spread the abrupt change over several samples, canceling part of the aliasing energy. A precomputed table or analytic expression provides the BLEP shape, allowing efficient real-time operation.

Variants include polyBLEP, which generalizes the idea to polyphonic or higher-order reconstructions by distributing the transition across multiple phases; this yields better anti-aliasing at higher frequencies. BLEP methods are widely used in software synthesizers and digital audio libraries where performance constraints preclude heavy oversampling while maintaining sound quality for common waveforms.

Limitations include dependence on the table size, sample rate, and oscillator frequency; at very high frequencies or near Nyquist, some residual aliasing may remain. See also aliasing reduction and band-limited synthesis.