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 mini- mized. 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 opti- mized individually for each mesh structure. We intr oduce an extended method called multiwarping, which can be used to fur- ther decrease the dispersion error. The frequency range of digital waveguide mesh simulations is also discussed.