L. Savioja et V. Valimaki, Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques, IEEE SPEECH, 8(2), 2000, pp. 184-194
The digital waveguide mesh is an extension of the one-dimensional (1-D) dig
ital waveguide technique. The mesh can be used for simulation of two- and t
hree-dimensional (3-D) wave propagation in musical instruments and acoustic
spaces. The original rectangular digital waveguide mesh algorithm suffers
from direction-dependent dispersion. Alternative geometries, such as the tr
iangular mesh, have been proposed previously to improve the performance of
the mesh. In this paper, we show that the dispersion problem may be reduced
using various other techniques. These methods include multidimensional int
erpolation, optimization of the point-spreading function, and frequency war
ping. We compare the accuracy and computational complexity of these techniq
ues in the two-dimensional (2-D) case and conduct numerical simulations of
a membrane. A rectangular mesh using second-order Lagrange interpolation ca
n be implemented without multiplications, but its accuracy is worse than th
at of other enhanced structures. The most accurate technique in terms of th
e relative frequency error is the warped triangular mesh whose maximum erro
r is 0.6%, The warped rectangular mesh with optimized weighting coefficient
s is not as exact, but still offers a 1.2% accuracy.