2-D DIGITAL WAVEGUIDE MESH TOPOLOGIES IN ROOM ACOUSTICS MODELLING

ABSTRACTDigital waveguide mesh models have provided an accurate andefficient method of modelling the properties of many resonantstructures, including acoustic spaces. 2-D rectilinear andtriangular mesh structures have been used extensively in the pastto model plates and membranes and are presented here aspotential analogues to 2-D acoustic spaces. Impulse responsemeasurements are taken and comparisons are made regarding thespectral content and the associated properties when comparedwith standard room acoustic parameters. Enhanced meshstructures are examined using frequency warping techniques andhigh-resolution sampling rates. The 2-D triangular mesh isshown to be considerably superior to the rectilinear mesh in termsof the measurements taken, with a further significantimprovement being made by using the same mesh oversampled toa much higher resolution to improve the bandwidth of themeasured impulse responses.1. INTRODUCTIONAll sounds have associated with them an environmental contextrelated to the acoustic space within which they are heard.Composers have long used and manipulated these properties ofsounds in space as a fundamental part of their music. Manymethods have been used to simulate the acoustics of an enclosedspace, and digital waveguide mesh models have provided anaccurate and efficient method of modelling this physicallycomplex system [1], [2], [3], [4]. However, due to the highsampling rate that is required to model even the smallest andsimplest acoustically interesting space, a 3-D mesh suitable forfull audio bandwidth processing is often impractical toimplement, resulting in prohibitively high computation times. Apartial compromise is sought by accurately modelling an acousticspace in the two dimensional plane only, in order to ascertainwhether or not a musically useful environmental context can besuccessfully synthesized [5].This paper examines some of the properties of two such 2-Dwaveguide mesh structures when used to model a simplerectangular 2-D representation of an enclosed space. Both therectilinear and triangular mesh structures have been usedextensively in the past to model plates and membranes [6], [7]and are presented here as potential analogues to 2-D acousticspaces. Impulse response measurements are taken andcomparisons are made regarding the spectral content and theassociated properties when compared with standard roomacoustic parameters. Suggestions are also made as to how these2-D models could be enhanced so as to improve the resultantacoustic environmental context.2. 2-D DIGITAL W AVEGUIDE MESH STRUCTURESA waveguide is any medium in which wave motion can becharacterised by the one-dimensional wave equation. In thelossless case, all solutions can be expressed in terms of left-goingand right-going travelling waves and can be simulated using a bi-directional digital delay line. A digital waveguide model isobtained by sampling, both in space and time, the one-directionaltravelling waves occuring in a system of ideal lossless waveguides[8]. The sampling points in this case are called scatteringjunctions, and are connected by bi-directional unit-delay digitalwaveguides [9]. Figure 1 shows the general case of a scatteringjunction J with N neighbours, i = 1,2,… N.The sound pressure in a waveguide is represented by p