Rounding Corners with BLAMP

Fabián Esqueda, Vesa Välimäki and Stefan Bilbao

Companion page for a paper in the 19th International Conference on Digital Audio Effect (DAFx-16),
Brno, Czech Republic, Sept 5 — 9, 2016


The use of the bandlimited ramp (BLAMP) function as an antialiasing tool for audio signals with sharp corners is presented. Discontinuities in the waveform of a signal or its derivatives require infinite bandwidth and are major sources of aliasing in the digital domain. A polynomial correction function is modeled after the ideal BLAMP function. This correction function can be used to treat aliasing caused by sharp edges or corners which translate into discontinuities in the first derivative of a signal. Four examples of cases where these discontinuities appear are discussed: synthesis of triangular waveforms, hard clipping, and half-wave and full-wave rectification. Results obtained show that the BLAMP function is a more efficient tool for alias reduction than oversampling. The polynomial BLAMP can reduce the level of aliasing components by up to 50 dB and improve the overall signal-to-noise ratio by about 20 dB. The proposed method can be incorporated into virtual analog models of musical systems.

The original paper is available here.

DAFx-16 Presentation Slides

You can download a PDF version of the DAFx-16 presentation slides here.

Sound Examples

Logarithmic Clipped Chirp

Logarithmic hard-clipped chirp before and after BLAMP correction:

Extracted aliases:

Clipped Flute Recording

Clipped flute recording before and after BLAMP correction:

Extracted aliases:

Clipped Guitar Recording

Hard-clipped guitar recording before and after BLAMP correction:

Extracted aliases:

Full-wave Rectified Logarithmic Chirp

Full-wave rectified logarithmic chirp before and after BLAMP correction

Matlab scripts

Example files that plot some of the figures shown in the paper and help understand how to use the proposed methods:

polyBLAMP_triangular Plots Figure 5, the antiliased triangular oscillator waveform.

polyBLAMP_clipping Plots Figure 7, antiliased clipped sinewave.

polyBLAMP_hw_rectifier Plots Figure 9, antiliased half-wave rectified sinewave.

polyBLAMP_hw_rectifier Plots Figure 11, antiliased half-wave rectified string signal. Requires string recording, available here.

You can also download all files as a single zip file by clicking here.