Interconnecting digital waveguides and finite difference structures: Recent advances

Abstract

Digital waveguides and finite difference schemes have been generally considered as alternative techniques in physical modeling of spatially distributed systems. The main difference between these techniques is in the variables used in the computation; in digital waveguide simulations traveling-wave components are used, whereas physical variables are typical in finite difference schemes. Although both techniques are known to provide exact modeling of ideal one-dimensional band-limited wave propagation and both of them can be composed to approximate higher-dimensional mesh structures, they usually become computationally different in the presence of losses, dispersion, and nonlinear interactions. Despite these differences, successful examples of hybrid waveguide/finite-difference models have been proposed in the literature. In these references, the finite-difference sections typically account for local nonlinear interactions. More recently, a general, unifying, and DSP-oriented framework is introduced, where the functional equivalence of digital waveguides and finite difference schemes is systematically elaborated and the conditions of building mixed models are studied. The present lecture will summarize the new framework and provide demonstrations of hybrid models. Real-time sound examples will be presented. [Work supported by EU ALMA project (IST-2001-33059).]