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

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.