Recent research in physical modeling of musical instruments for purposes of sound synthesis is reviewed. Recent references, results, and outstanding problems are highlighted for models of strings, winds, brasses, percussion, and acoustic spaces. Emphasis is placed on digital waveguide models and the musical acoustics research on which they are based.

The feedback delay network (FDN) has been proposed for digital reverberation. Also proposed with similar advantages is the digital waveguide network (DWN). This paper notes that the commonly used FDN with an N × N orthogonal feedback matrix is isomorphic to a normalized digital waveguide network consisting of one scattering junction and a vector transformer joining N reflectively terminated branches. Generalizations of FDNs and DWNs are discussed. The general case of a losslessness FDN feedback matrix is shown to be any matrix having unit-modulus eigenvalues and linearly independent eigenvectors. A special class of FDNs using circulant matrices is proposed. These structures can be efficiently implemented and allow control of the time and frequency behavior. Applications of circulant feedback delay networks in

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. 1.

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While visual rendering of buildings is the state of the art in today's design programs, acoustic or auditory rendering is still in its infancy. This paper reviews some promising approaches to the computer simulation of sound propagation and perception in buildings. The range of methods spans from the numerical solution of the wave equation to advanced geometric methods based on ray tracing and radiosity algorithms. Furthermore concepts for modelling the human sound perception are discussed. Finally some issues of practical implementation will be addressed. 1. INTRODUCTION It is a common feature of modern computer aided design programs to reward the user with a photorealistic rendering of the prospective building. However despite all visual perfection, the auditory component is completely missing. There is no impression of the room acoustics, no assessment of the noise level in offices or workshops and no evaluation of the effect of sound absorbing materials by computer simulation. It ...

We present a computational acoustics approach to the computer simulation of sound elds. It is based on physical modelling of sound wave propagation in terms of the partial dierential equations for sound pressure and particle velocity. A step by step procedure is given to convert the partial dierential equation description into a suitable form for numerical integration. The resulting discrete model is derived with methods from numerical mathematics, linear algebra, and multidimensional system theory and formulated in terms of a state space representation. The treatment of boundary conditions and examples are presented in a companion paper. 2 1 Introduction Problems in active noise control and acoustic echo cancellation are almost exclusively considered from the point of view of adaptive control systems [4, 7, 9]. The emphasis in active noise control system design is placed on nding appropriate positions of sensors and actors and on the design of fast adaptive control algorithms. ...

In concert hall acoustics, the reflection characteristics of the ceiling and the walls are important for minimizing the interaural cross correlation. Many design methods have been presented so far in order to design highly diffusing surfaces. This paper presents a two-dimensional digital waveguide mesh having a highly diffusing boundary using quadratic residue sequences, and illustrates its reflection properties. Empirical analyses show that high diffusion occurs at the diffusing boundary, and the scattering characteristics show the energy of an incident plane wave is evenly scattered in a mesh with a diffusing boundary while a specular reflection occurs in a mesh with flat surfaces. 1

this paper reviews two applications in digital waveguide modeling: single reed woodwinds (such as the clarinet), and bowed strings (such as the violin). In these applications, a sustained sound is synthesized by the interaction of the digital waveguide with a nonlinear junction causing spontaneous, self-sustaining oscillation in response to an applied mouth pressure or bow velocity, respectively. This type of nonlinear oscillation forms the basis of the Yamaha "VL" series of synthesizers ("VL" standing for "virtual lead"). 2 Single-Reed Instruments

The two main approaches for room acoustic modeling are the wave-based and the ray-based techniques. In this paper we briefly overview the digital waveguide mesh method which is a wave-based model operating in the time domain. As a case study we show visualizations of edge diffraction modeled with the waveguide mesh technique. Some preliminary analysis of computational requirements for real-time auralizations are also presented, and the idea of frequency domain hybrid model is revisited. 1

Characteristics of digital waveguide meshes with more than three physical dimensions are studied. Especially, the properties of a 4-D mesh are analyzed and compared to waveguide structures of lower dimensionalities. The hypermesh produces a response with a dense and irregular modal pattern at high frequencies, which is beneficial in modeling the reverberation of rooms or musical instrument bodies. In addition, it offers a high degree of decorrelation between output points selected at different locations, which is advantageous for multi-channel reverberation. The frequency-dependent decay of the hypermesh response can be controlled using boundary filters introduced recently by one of the authors. Several hypermeshes can be effectively combined in a multirate system, in which each mesh produces reverberation on a finite frequency band. The paper presents three hypermesh application examples: a multi-channel reverberation algorithm, the modeling of the impulse response of a lecture hall, and the simulation of the response of a clavichord soundbox.