Recent Progress in Wave Digital Audio Effects

The digital audio effects (DAFx) community has contributed significantly to advancements in ``virtual analog'' modeling of classic audio effects in software. Practicing musicians have enjoyed a growing list of classic analog gear available now as digital audio plugins as a result.

One competitive approach is the Wave Digital Filters (WDF) formulation pioneered by Alfred Fettweis. WDFs have been around since the early 1970s and have found much use in VLSI implementations of digital filters, where superior numerical robustness is especially important. Since the early 2000s, this framework has been applied increasingly to musical acoustic modeling and digital audio effects, and its range of applicability has been recently expanded considerably to include arbitrary circuit topologies and multiple nonlinear elements.

The closely-related Digital Waveguide Framework (DWF) similarly uses wave variables (traveling-wave components) because wave-propagation delay lines can be implemented super efficiently as circular buffers. As a result, it is straightforward to combine these two paradigms to yield wave-variable models of a mixture of distributed and lumped systems, such as a lumped hammer model striking waveguide string in the case of a piano model.

WDFs use wave variables in the context of lumped modeling where, by definition, wave propagation does not occur. How then can we understand the use of wave variables in WDFs? This talk includes a somewhat alternative development of WDF principles based on the way that wave variables can be used to resolve implicit relationships in modular discrete circuit models.

The complexity of audio circuitry has often stressed the state of the art of WDFs, especially for nonlinear models. The DAFx community has contributed many new techniques in response. This talk will review these contributions and point out remaining issues for future research in WDF theory.

In addition to their theoretical appeal, desirable energetic/numerical properties, and fine-grained modeling fidelity, WDFs are also attractive to virtual-analog algorithm designers as an elegant modular software framework. Implementing WDFs as a hierarchical object-orient tree in software such as C++ can yield readable and reusable code, with clear high-level descriptions of circuits and digital audio processing. We include examples of practical wave digital modeling, and demonstrations of real-time performance.