Paper Archive

Antiderivative Antialiasing (ADAA), has become a pivotal method for reducing aliasing when dealing with nonlinear function at audio rate. However, its implementation requires analytical computation of the antiderivative of the nonlinear function, which in practical cases can be challenging without a symbolic solver. Moreover, when the nonlinear function is given by measurements it must be approximated to get a symbolic description. In this paper, we propose a simple approach to ADAA for practical applications that employs numerical integration of lookup tables (LUTs) to approximate the antiderivative. This method eliminates the need for closed-form solutions, streamlining the ADAA implementation process in industrial applications. We analyze the trade-offs of this approach, highlighting its computational efficiency and ease of implementation while discussing the potential impact of numerical integration errors on aliasing performance. Experiments are conducted with static nonlinearities (tanh, a simple wavefolder and the Buchla 259 wavefolding circuit) and a stateful nonlinear system (the diode clipper).

Download

Nonlinear digital circuits and waveshaping are active areas of study, specifically for what concerns numerical and aliasing issues. In the past, an effective method was proposed to discretize nonlinear static functions with reduced aliasing based on the antiderivative of the nonlinear function. Such a method is based on the continuoustime convolution with an FIR antialiasing filter kernel, such as a rectangular kernel. These kernels, however, are far from optimal for the reduction of aliasing. In this paper we introduce the use of arbitrary IIR rational transfer functions that allow a closer approximation of the ideal antialiasing filter, required in the fictitious continuous-time domain before sampling the nonlinear function output. These allow a higher degree of aliasing reduction and can be flexibly adjusted to balance performance and computational cost.

Download