Reduction of the dispersion error in the interpolated digital waveguide mesh using frequency warping

Abstract

The digital waveguide mesh is an extension of the one-dimensional digital waveguide technique. The mesh is used for simulation of two-and three-dimensional wave propagation in musical instruments and acoustic spaces. The rectangular digital waveguide mesh algorithm suffers from direction-dependent dispersion. By using the interpolated mesh, nearly uniform wave propagation characteristics are obtained in all directions. In this paper we show how the dispersion error of the interpolated mesh can be reduced by frequency warping. By using this technique the bandwidth where the frequency accuracy is within 1% tolerance is more than doubled.

Virtual Acoustic Musical Instruments: Review and Update

“…Highly efficient computational models of 2D membranes and 3D volumes may be built using the digital waveguide mesh [62,182,180,183]. More recently, Lauri and Välimäki have developed a frequency warping approach to compensating for dispersive wave propagation in a variety of mesh types [132,133,134]. The 2001 thesis of Bilbao [25] provides a unified view of the digital waveguide mesh and wave digital filters [60] as particular classes of energy invariant finite difference schemes [168].…”