Virtual analog models of the Lockhart and Serge wavefolders

Wavefolders are a particular class of nonlinear waveshaping circuits, and a staple of the "West Coast" tradition of analog sound synthesis. In this paper, we present analyses of two popular wavefolding circuits-the Lockhart and Serge wavefolders-and show that they achieve a very similar audio effect. We digitally model the input-output relationship of both circuits using the Lambert-W function, and examine their time- and frequency-domain behavior. To ameliorate the issue of aliasing distortion introduced by the nonlinear nature of wavefolding, we propose the use of the first-order antiderivative method. This method allows us to implement the proposed digital models in real-time without having to resort to high oversampling factors. The practical synthesis usage of both circuits is discussed by considering the case of multiple wavefolder stages arranged in series.