Practical Virtual Analog Modeling Using MÖbius Transforms

Abstract

MÖbius transforms provide for the definition of a family of one-step discretization methods offering a framework for alleviating well-known limitations of common one-step methods, such as the trapezoidal method, at no cost in model compactness or complexity. In this paper, we extend the existing theory around these methods. Here, we show how it can be applied to common frameworks used to structure virtual analog models. Then, we propose practical strategies to tune the transform parameters for best simulation results. Finally, we show how such strategies enable us to formulate much improved non-oversampled virtual analog models for several historical audio circuits.