Numerical integration of linear and nonlinear ordinary and partial differential equations describing physically realistic systems can be achieved by means of principles derived from those originally developed in the context of wave digital filters, thus in a specialized branch of the broader area of digital signal processing The method draws maximum advantage of essential physical properties of such systems, in particular of causality, passivity, finiteness of propagation velocities etc and makes use of the trapezoidal rule for approximating the differential operators This way it has the unique advantage of simultaneously offering second-order accuracy, high robustness and fault tolerance, massive parallelism, full localness (also for taking into account arbitrary boundary conditions and shapes), and explicit or at least semi-explicit computability A brief overview of the method is given

Robust Numerical Integration Using Wave-Digital Concepts

We show how to construct an object-based environment for sound generation, whose objects can be individually synthesized and which can interact with each other through modelling of a potential interaction topology. We show how this interaction topology can be mode dynamic and time-varying. We also discuss how we envision an object-based environment that integrates geometric, radiometric, and intrinsic/extrinsic acoustic properties. We finally illustrate our first results towards modelling of complex sound generation systems.

Object-based sound synthesis for virtual environments-using musical acoustics

The propagation of sound waves is described by partial differential equations for the acoustic pressure and the acoustic fluid velocity. The solution depends on the shape of the enclosure and on the boundary conditions. Among various methods for the discretization of partial differential equations, the multidimensional wave digital filter approach is known to yield robust algorithms for the discrete simulation of continuous problems. This paper describes the derivation of a discrete model for three-dimensional sound propagation according to multidimensional wave digital filtering principles. The correct treatment of boundary conditions for various wall impedances is shown. A numerical example for the sound propagation in three interconnected rooms of a building demonstrates the capabilities of the method.

Simulation of three-dimensional sound propagation with multidimensional wave digital filters

Simulation of wave propagation by multidimensional digital filters

A new approach is proposed that closely synthesizes tones of plucked string instruments by using a class of physical modeling recurrent networks. The strategies employed consist of a fast training algorithm and a multistage training procedure that are able to obtain the synthesis parameters for a specific instrument automatically. The training vector can be recorded tones of most target plucked instruments with ordinary microphones. The proposed approach delivers encouraging results when it is applied to different types of plucked string instruments such as steel-string guitar, nylon-string guitar, harp, Chin, Yueh-chin, and Pipa. The synthesized tones sound very close to the originals produced by their acoustic counterparts. In addition, the paper presents an embedded technique that can produce special effects such as vibrato and portamento that are vital to the playing of plucked-string instruments. The computation required in the resynthesis processing is also reasonable.

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A class of physical modeling recurrent networks for analysis/synthesis of plucked string instruments

The application of multidimensional wave digital filter principles to the numerical solution of partial differential equations has been introduced in various recent publications. However, the examples presented so far do not explicitly consider boundary conditions. This letter shows how to incorporate boundary values into a multidimensional wave digital filter. A lossy transmission line of finite extent with given terminations is chosen as an example. >

R. Rabenstein

Papers

Application of multidimensional wave digital filters to boundary value problems