Signal-Theoretic Characterization of Waveguide Mesh Geometries for Models of Two--Dimensional Wave Propagation in Elastic Media

Waveguide Meshes are efficient and versatile models of wave propagation along a multidimensional ideal medium. The choice of the mesh geometry affects both the computational cost and the accuracy of simulations. In this paper, we focus on 2D geometries and use multidimensional sampling theory to compare the square, triangular, and hexagonal meshes in terms of sampling efficiency and dispersion error under conditions of critical sampling. The analysis shows that the triangular geometry exhibits the most desirable tradeoff between accuracy and computational cost.Comment: 9 pages, 6 figures, 1 table, to appear on IEEE Transactions on Speech and Audio Processing, vol. 9, no. 2, february 200

Online Correction of Dispersion Error in 2D Waveguide Meshes

An elastic ideal 2D propagation medium, i.e., a membrane, can be simulated by models discretizing the wave equation on the time-space grid (finite difference methods), or locally discretizing the solution of the wave equation (waveguide meshes). The two approaches provide equivalent computational structures, and introduce numerical dispersion that induces a misalignment of the modes from their theoretical positions. Prior literature shows that dispersion can be arbitrarily reduced by oversizing and oversampling the mesh, or by adpting offline warping techniques. In this paper we propose to reduce numerical dispersion by embedding warping elements, i.e., properly tuned allpass filters, in the structure. The resulting model exhibits a significant reduction in dispersion, and requires less computational resources than a regular mesh structure having comparable accuracy.Comment: 4 pages, 5 figures, to appear in the Proceedings of the International Computer Music Conference, 2000. Corrected first referenc

The KW-boundary hybrid digital waveguide mesh for room acoustics applications

The digital waveguide mesh is a discrete-time simulation used to model acoustic wave propagation through a bounded medium. It can be applied to the simulation of the acoustics of rooms through the generation of impulse responses suitable for auralization purposes. However, large-scale three-dimensional mesh structures are required for high quality results. These structures must therefore be efficient and also capable of flexible boundary implementation in terms of both geometrical layout and the possibility for improved mesh termination algorithms. The general one-dimensional N-port boundary termination is investigated, where N depends on the geometry of the modeled domain and the mesh topology used. The equivalence between physical variable Kirchoff-model, and scattering-based wave-model boundary formulations is proved. This leads to the KW-hybrid one-dimensional N-port boundary-node termination, which is shown to be equivalent to the Kirchoff- and wave-model cases. The KW-hybrid boundary-node is implemented as part of a new hybrid two-dimensional triangular digital waveguide mesh. This is shown to offer the possibility for large-scale, computationally efficient mesh structures for more complex shapes. It proves more accurate than a similar rectilinear mesh in terms of geometrical fit, and offers significant savings in processing time and memory use over a standard wave-based model. The new hybrid mesh also has the potential for improved real-world room boundary simulations through the inclusion of additional mixed modeling algorithms

Waveguide physical modeling of vocal tract acoustics: flexible formant bandwidth control from increased model dimensionality

Digital waveguide physical modeling is often used as an efficient representation of acoustical resonators such as the human vocal tract. Building on the basic one-dimensional (1-D) Kelly-Lochbaum tract model, various speech synthesis techniques demonstrate improvements to the wave scattering mechanisms in order to better approximate wave propagation in the complex vocal system. Some of these techniques are discussed in this paper, with particular reference to an alternative approach in the form of a two-dimensional waveguide mesh model. Emphasis is placed on its ability to produce vowel spectra similar to that which would be present in natural speech, and how it improves upon the 1-D model. Tract area function is accommodated as model width, rather than translated into acoustic impedance, and as such offers extra control as an additional bounding limit to the model. Results show that the two-dimensional (2-D) model introduces approximately linear control over formant bandwidths leading to attainable realistic values across a range of vowels. Similarly, the 2-D model allows for application of theoretical reflection values within the tract, which when applied to the 1-D model result in small formant bandwidths, and, hence, unnatural sounding synthesized vowels

Acoustic modeling using the digital waveguide mesh

The digital waveguide mesh has been an active area of music acoustics research for over ten years. Although founded in 1-D digital waveguide modeling, the principles on which it is based are not new to researchers grounded in numerical simulation, FDTD methods, electromagnetic simulation, etc. This article has attempted to provide a considerable review of how the DWM has been applied to acoustic modeling and sound synthesis problems, including new 2-D object synthesis and an overview of recent research activities in articulatory vocal tract modeling, RIR synthesis, and reverberation simulation. The extensive, although not by any means exhaustive, list of references indicates that though the DWM may have parallels in other disciplines, it still offers something new in the field of acoustic simulation and sound synth

Real-time dynamic articulations in the 2-D waveguide mesh vocal tract model

Time domain articulatory vocal tract modeling in one-dimensional (1-D) is well established. Previous studies into two-dimensional (2-D) simulation of wave propagation in the vocal tract have shown it to present accurate static vowel synthesis. However, little has been done to demonstrate how such a model might accommodate the dynamic tract shape changes necessary in modeling speech. Two methods of applying the area function to the 2-D digital waveguide mesh vocal tract model are presented here. First, a method based on mapping the cross-sectional area onto the number of waveguides across the mesh, termed a widthwise mapping approach is detailed. Discontinuity problems associated with the dynamic manipulation of the model are highlighted. Second, a new method is examined that uses a static-shaped rectangular mesh with the area function translated into an impedance map which is then applied to each waveguide. Two approaches for constructing such a map are demonstrated; one using a linear impedance increase to model a constriction to the tract and another using a raised cosine function. Recommendations are made towards the use of the cosine method as it allows for a wider central propagational channel. It is also shown that this impedance mapping approach allows for stable dynamic shape changes and also permits a reduction in sampling frequency leading to real-time interaction with the model

Physics-based models for the acoustic representation of space in virtual environments

In questo lavoro sono state affrontate alcune questioni inserite nel tema pi\uf9 generale della rappresentazione di scene e ambienti virtuali in contesti d\u2019interazione uomo-macchina, nei quali la modalit\ue0 acustica costituisca parte integrante o prevalente dell\u2019informazione complessiva trasmessa dalla macchina all\u2019utilizzatore attraverso un\u2019interfaccia personale multimodale oppure monomodale acustica. Pi\uf9 precisamente \ue8 stato preso in esame il problema di come presentare il messaggio audio, in modo tale che lo stesso messaggio fornisca all\u2019utilizzatore un\u2019informazione quanto pi\uf9 precisa e utilizzabile relativamente al contesto rappresentato. Il fine di tutto ci\uf2 \ue8 riuscire a integrare all\u2019interno di uno scenario virtuale almeno parte dell\u2019informazione acustica che lo stesso utilizzatore, in un contesto stavolta reale, normalmente utilizza per trarre esperienza dal mondo circostante nel suo complesso. Ci\uf2 \ue8 importante soprattutto quando il focus dell\u2019attenzione, che tipicamente impegna il canale visivo quasi completamente, \ue8 volto a un compito specifico.This work deals with the simulation of virtual acoustic spaces using physics-based models. The acoustic space is what we perceive about space using our auditory system. The physical nature of the models means that they will present spatial attributes (such as, for example, shape and size) as a salient feature of their structure, in a way that space will be directly represented and manipulated by means of them

Modeling Sparsely Reflecting Outdoor Acoustic Scenes using the Waveguide Web

Computer games and virtual reality require digital reverberation algorithms, which can simulate a broad range of acoustic spaces, including locations in the open air. Additionally, the detailed simulation of environmental sound is an area of significant interest due to the propagation of noise pollution over distances and its related impact on well-being, particularly in urban spaces. This paper introduces the waveguide web digital reverberator design for modeling the acoustics of sparsely reflecting outdoor environments; a design that is, in part, an extension of the scattering delay network reverberator. The design of the algorithm is based on a set of digital waveguides connected by scattering junctions at nodes that represent the reflection points of the environment under study. The structure of the proposed reverberator allows for accurate reproduction of reflections between discrete reflection points. Approximation errors are caused when the assumption of point-like nodes does not hold true. Three example cases are presented comparing waveguide web simulated impulse responses for a traditional shoebox room, a forest scenario, and an urban courtyard, with impulse responses created using other simulation methods or from real-world measurements. The waveguide web algorithm can better enable the acoustic simulation of outdoor spaces and so contribute toward sound design for virtual reality applications, gaming, and auralization, with a particular focus on acoustic design for the urban environment