Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques

Abstract

The digital waveguide mesh is an extension of the one-dimensional (1-D) digital waveguide technique. The mesh can be used for simulation of two- and three-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 triangular 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 interpolation, optimization of the point-spreading function, and frequency warping. We compare the accuracy and computational complexity of these techniques in the two-dimensional (2-D) case and conduct numerical simulations of a membrane. A rectangular mesh using second-order Lagrange interpolation can be implemented without multiplications, but its accuracy is worse than that of other enhanced structures. The most accurate technique in terms of the relative frequency error is the warped triangular mesh whose maximum error is 0.6%. The warped rectangular mesh with optimized weighting coefficients is not as exact, but still offers a 1.2% accuracy.