Aspects of Digital Waveguide Networks for Acoustic Modeling Applications

This paper collects together various facts about digital waveguide networks (DWN) used in acoustic modeling, particularly results pertaining to lossless scattering at the junction of N intersecting digital waveguides. Applications discussed include music synthesis based on physical models and delay effects such as artificial reverberation. Connections with Wave Digital Filters (WDF), ladder/lattice digital filters, and other related topics are outlined. General conditions for losslessness and passivity are specified. Computational complexity and dynamic range requirements are addressed. Both physical and algebraic analyses are utilized. The physical interpretation leads to many of the desirable properties of DWNs. Using both physical and algebraic approaches, three new normalized ladder filter structures are derived which have only three multiplications per two-port scattering junction instead of the four required in the well known version. A vector scattering formulation is derived which maximizes generality subject to maintaining desirable properties. Scattering junctions are generalized to allow any waveguide to have a complex wave impedance which is equivalent at the junction to a lumped load impedance, thus providing a convenient bridge between lumped and distributed modeling methods. Junctions involving complex wave impedances yield generalized scattering coefficients which are frequency dependent and therefore implemented in practice using digital filters. Scattering filters are typically isolable to one per junction in a manner analogous to the multiply in a one-multiply lattice-filter section. ∗http://ccrma.stanford.edu/