Wave Digital Filter Tutorial—Part I

Come one, come all, to the first of a three-part tutorial series on everyone's favorite lumped system discretization formalism: Wave Digital Filters (WDFs)! Alfred Fettweis originated WDFs as a filter design technique in 1970; since the early 2000s researchers have extended his approach to simulate lumped acoustic systems (e.g., piano hammers, clarinet reed) and classic audio circuitry (e.g. effect pedals, guitar amps). Though powerful, WDFs can be confusing. In this tutorial, Ph.D. candidate Kurt James Werner will start from scratch, telling you everything you need to know about the sometimes puzzling and notoriously self-contained WDF literature.

Wave Digital Filters are an active research area at CCRMA. The efforts of CCRMA researchers (including Kurt James Werner, Vaibhav Nangia, prof. Julius O. Smith, and prof. Jonathan Abel) over the last year and a half have resulted in 5 CCRMA-led conference papers [1]–[5] (one of which won best student paper at WASPAA [4]!), 2 more conference papers [6]–[7] and a journal article submission [8] in collaboration with Alberto Bernardini and prof. Augusto Sarti from the Politecnico di Milano, a keynote presentation at DAFx [9], an invited plenary talk at a EURASIP workshop [10], and various other talks around CCRMA and the bay area. Meanwhile, Ross Dunkel, Maximillian Rest, and Mike Olsen have entered the fray and are already contributing to the next round of research. You could be next!

"Wave Digital Filter Tutorial—Part 2" will be coming soon, covering classical WDF techniques for handling nonlinearities.

References
[1] Kurt James Werner, Julius O. Smith, and Jonathan S. Abel, "Wave Digital Filter Adaptors for Arbitrary Topologies and Multiport Linear Elements," in Proceedings of the International Conference on Digital Audio Effects (DAFx-15), Trondheim, Norway, November 30 – December 3 2015.
[2] Kurt James Werner, Vaibhav Nangia, Julius O. Smith, and Jonathan S. Abel, "Resolving Wave Digital Filters with Multiple/Multiport Nonlinearities," in Proceedings of the International Conference on Digital Audio Effects (DAFx-15), Trondheim, Norway, November 30 – December 3 2015.
[3] Kurt James Werner, Vaibhav Nangia, Alberto Bernardini, Julius O. Smith, and Augusto Sarti, "An Improved and Generalized Diode Clipper Model for Wave Digital Filters," in Proceedings of the 139th Convention of the Audio Engineering Society (AES), New York, NY, October 29 – November 1 2015.
[4] Kurt James Werner, Vaibhav Nangia, Julius O. Smith, and Jonathan S. Abel, "A General and Explicit Formulation for Wave Digital Filtres with Multiple/Multiport Nonlinearities and Complicated Topologies," in Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), New Paltz, NY, October 18–21 2015. (awarded best student paper)
[5] Kurt James Werner and Julius O. Smith, "An Energetic Interpretation of Nonlinear Wave Digital Filter Lookup Table Error," in Proceedings of the IEEE International Symposium on Signals, Circuits, and Systems (ISSCS), Iasi, Romania, July 9–10 2015. (invited paper)
[6] Alberto Bernardini, Kurt James Werner, Augusto Sarti, and Julius O. Smith, "Modeling a Class of Multi-Port NonLinearities in Wave Digital Structures," in Proceedings of the European Signal Processing Conference (EUSIPCO), Nice, France, August 31 – September 4 2015.
[7] Alberto Bernardini, Kurt James Werner, Augusto Sarti, and Julius O. Smith, "Multi-Port NonLinearities in Wave Digital Structures," in Proceedings of the IEEE International Symposium on Signals, Circuits, and Systems (ISSCS), Iasi, Romania, July 9–10 2015.
[8] Alberto Bernardini, Kurt James Werner, Augusto Sarti, and Julius O. Smith, "Modeling Nonlinear Wave Digital Elements using the Lambert Function," in submission.
[9] Julius O. Smith and Kurt James Werner, "Recent Progress in Wave Digital Audio Effects," at International Conference on Digital Audio Effects (DAFx-15), Trondheim, Norway, November 30 – December 3 2015. (invited keynote talk)
[10] Julius O. Smith and Kurt James Werner, "Recent Developments in Signal Processing for Audio and Music," at EURASIP International Workshop on Recent Trends in Signal Processing (RTSP), Cluj-Napoca, Romania, July 6–7 2015. (invited plenary talk)