Fixed-rate Modeling of Audio Lumped Systems: A Comparison Between Trapezoidal and Implicit Midpoint Methods
This paper presents a comparison framework to study the relative benefits of the typical trapezoidal method with the lesser-used implicit midpoint method for the simulation of audio lumped systems at a fixed rate. We provide preliminary tools for understanding the behavior and error associated with each method in connection with typical analysis approaches. We also show implementation strategies for those methods, including how an implicit midpoint method solution can be generated from a trapezoidal method solution and vice versa. Finally, we present some empirical analysis of the behavior of each method for a simple diode clipper circuit and provide an approach to help interpret their relative performance and how to pick the more appropriate method depending on desirable properties. The presented tools are also intended as a general approach to interpret the performance of discretization approaches at large in the context of fixed-rate simulation.