Recent Extensions to Topological and Nonlinear Aspects of Wave Digital Filter Theory

The Wave Digital Filter approach can be used to create computational models of lumped reference systems, including rectilinear mechanical, rotational mechanical, acoustical, and electronic systems. When they are applicable, Wave Digital Filters enjoy properties including modularity, accuracy, and guaranteed incremental passivity that make them attractive in the context of musical instrument and audio effect simulation. However, the class of reference systems that can be modeled with Wave Digital Filters has historically been restricted to systems with simple topologies (which can be decomposed entirely into series and parallel connections) and which contain only a single “nonadaptable” element (e.g., a diode, ideal source, or switch). This talk details recent Wave Digital Filter advances from Stanford University's Center for Computer Research in Music and Acoustics (CCRMA), which broaden the applicability of Wave Digital Filters to reference systems with any topology and an arbitrary number of nonlinearities or other nonadaptable elements. These advances have enabled many new and previously intractable musical circuit simulations at CCRMA, including active tone stages and transistor/diode/feedback clipping from guitar distortion pedals, the electromechanical Hammond organ vibrato/chorus system, guitar tube pre-amplifiers and tone stacks, circuits involving operational amplifiers, drum machine circuits, and transistor amplifiers.