Interpolated and Warped 2-d Digital Waveguide Mesh Algorithms

Interpolated and warped digital waveguide mesh algorithms have been developed to overcome the problem caused by direction and frequency-dependence of wave travel speed in digital waveguide mesh simulations. This paper reviews the interpolation methods applicable in the two-dimensional case. The bilinear interpolation technique and two other approaches are briefly recapitulated. The use of 2-D quadratic interpolation results in a mesh structure that is efficiently implemented using only additions and binary shifts. The optimized interpolated 2-D mesh is obtained by choosing the free parameters of the interpolation method so that the difference in wave travel speed in the axial and diagonal directions is minimized. The output signal of any digital waveguide mesh can be processed with a warped FIR filter to reduce the dispersion error at all frequencies. The frequency-warping factor must be optimized individually for each mesh structure. We introduce an extended method called multiwarping, which can be used to further decrease the dispersion error. The frequency range of digital waveguide mesh simulations is also discussed.