Simplifying antiderivative antialiasing with lookup table integration

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).