Recent Developments

An interesting approach to dispersion compensation is based on frequency-warping the signals going into the mesh [399]. Frequency warping can be used to compensate frequency-dependent dispersion, but it does not address angle-dependent dispersion. Therefore, frequency-warping is used in conjunction with an isotropic mesh.

The 3D waveguide mesh [518,521,399] is seeing more use for efficient simulation of acoustic spaces [396,182]. It has also been applied to statistical modeling of violin body resonators in [203,202,422,428], in which the digital waveguide mesh was used to efficiently model only the ``reverberant'' aspects of a violin body's impulse response in statistically matched fashion (but close to perceptually equivalent). The ``instantaneous'' filtering by the violin body is therefore modeled using a separate equalizer capturing the important low-frequency body and air modes explicitly. A unified view of the digital waveguide mesh and wave digital filters (§F.1) as particular classes of energy invariant finite difference schemes (Appendix D) appears in [54]. The problem of modeling diffusion at a mesh boundary was addressed in [268], and maximally diffusing boundaries, using quadratic residue sequences, was investigated in [279]; an introduction to this topic is given in §C.14.6 below.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.