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

Abstract

The digital waveguide mesh has been successfully used for simulation of two-dimensional (2-D) and threedimensional (3-D) wave propagation in musical instruments and acoustic spaces. Nevertheless, digital waveguide mesh algorithms suffer from dispersion which increases with frequency. In this letter, we show how the dispersion error of the triangular digital waveguide mesh can be reduced by frequency warping. By using this technique, the worst-case dispersion error of 0.6% is obtained, whereas in the original triangular mesh it is about 6.5%.

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

“…The interpolation technique works for rectangular 3-D meshes as shown in [12] and finding the appropriate warping factor should be straightforward. The warping technique is suitable for triangular digital waveguide mesh algorithms as well [18]. In this paper we have shown that the 1% accurate bandwidth of 2-D digital waveguide mesh simulations can be extended with the interpolated warped structure when compared with the original one.…”

On-Line Simulation of 2D Resonators with Reduced Dispersion Error using Compact Implicit Finite Difference Methods

“…A nearly frequencyindependent dispersion error can be achieved by setting b = 1 6 , which effectively gives the nearly isotropic scheme described by Trefethen [11]. The interpolated digital waveguide mesh developed by Savioja and Välimäki [4] uses the same stencil, but the coefficients of their difference equation are calculated using an optimisation method; this is effectively equivalent to setting b = 0.1879.…”

“…In the original rectangular twodimensional digital waveguide mesh (DWG), which is mathematically equivalent to a compact explicit FD scheme, this error is particularly severe in axial directions [3]. In order to make the error of the rectangular mesh homogeneous in all directions, interpolation techniques have been introduced [4], which make the dispersion error nearly direction-independent This research has been supported by the European Social Fund. [5].…”

Signal-theoretic characterization of waveguide mesh geometries for models of two-dimensional wave propagation in elastic media

“…Numerical dispersion cannot be completely eliminated, but it can be arbitrarily reduced increasing the density of the elements, and minimized choosing the "least dispersive geometry". Moreover, interpolation schemes [10] or off-line warping techniques [11] can be applied to attenuate the effects of numerical dispersion.…”