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

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

The modeling of diffuse boundaries in the 2-D digital waveguide mesh

The digital waveguide mesh can be used to simulate the propagation of sound waves in an acoustic system. The accurate simulation of the acoustic characteristics of boundaries within such a system is an important part of the model. One significant property of an acoustic boundary is its diffusivity. Previous approaches to simulating diffuse boundaries in a digital waveguide mesh are effective but exhibit limitations and have not been analyzed in detail. An improved technique is presented here that simulates diffusion at boundaries and offers a high degree of control and consistency. This technique works by rotating wavefronts as they pass through a special diffusing layer adjacent to the boundary. The waves are rotated randomly according to a chosen probability function and the model is lossless. This diffusion model is analyzed in detail, and its diffusivity is quantified in the form of frequency dependent diffusion coefficients. The approach used to measuring boundary diffusion is described here in detail for the 2-D digital waveguide mesh and can readily be extended for the 3-D case

Contributions to discrete-time methods for room acoustic simulation

The sound field distribution in a room is the consequence of the acoustic properties of radiating sources and the position, geometry and absorbing characteristics of the surrounding boundaries in an enclosure (boundary conditions). Despite there existing a consolidated acoustic wave theory, it is very difficult, nearly impossible, to find an analytical expression of the sound variables distribution in a real room, as a function of time and position. This scenario represents as an inhomogeneous boundary value problem, where the complexity of source properties and boundary conditions make that problem extremely hard to solve. Room acoustic simulation, as treated in this thesis, comprises the algebraical approach to solve the wave equation, and the way to define the boundary conditions and source modeling of the scenario under analysis. Numerical methods provide accurate algorithms for this purpose and among the different possibilities, the use of discrete-time methods arises as a suitable solution for solving those partial differential equations, particularized by some specific constrains. Together with the constant growth of computer power, those methods are increasing their suitability for room acoustic simulation. However, there exists an important lack of accuracy in the definition of some of these conditions so far: current frequency-dependent boundary conditions do not comply with any physical model, and directive sources in discrete-time methods have been hardly treated. This thesis discusses about the current state-of-the-art of the boundary conditions and source modeling in discrete-time methods for room acoustic simulation, and it contributes some algorithms to enhance boundary condition formulation, in a locally reacting impedance sense, and source modelling in terms of directive sources under a defined radiation pattern. These algorithms have been particularized to some discrete-time methods such as the Finite Difference Time Domain and the Digital Waveguide Mesh.Escolano Carrasco, J. (2008). Contributions to discrete-time methods for room acoustic simulation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8309Palanci

On the Equivalence of the Digital Waveguide and Finite Difference Time Domain Schemes

It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variables in a DW simulation. Since boundary conditions and initial values are more intuitively transparent in the DW formulation, the simple means of converting back and forth can be useful in initializing and constructing boundaries for FDTD simulations.Comment: v1: 6 pages; v2: 7 pages, generally more polished, more examples, expanded discussion; v3: 15 pages, added state space formulation, analysis of inputs and boundary conditions, translation of passive boundary conditions; v4: various typos fixe

Wayverb: A Graphical Tool for Hybrid Room Acoustics Simulation

Acoustic simulation aims to predict the behaviour of sound in a particular space. These simulations can be carried out on commodity computing hardware, and are faster, cheaper, and more convenient than building and recording a physical space. This is useful to architects, who need to know that their designs will meet exacting specifications before building starts. It is also useful to musicians and sound designers, who can use the simulation results to create pleasing, precise, and immersive audio effects. Currently, users are limited in their choice of simulation software, as existing solutions focus either on speed or on overall accuracy. Fast simulation techniques are often inaccurate at low frequencies, while more accurate techniques become prohibitively slow at higher frequencies. There is a clear need for a program which is fast, accurate at all frequencies, and easy to use without specialist training. This project identifies a hybrid acoustic simulation technique which combines the efficiency of geometric simulation with the accuracy of wave-based modelling. This fusion of simulation techniques, not available in any existing piece of simulation software, gives the user the flexibility to balance accuracy against efficiency as they require. This hybrid method is implemented in the Wayverb program. The program is made free and open-source, with a simple graphical interface, differentiating it from hybrid simulators found in the literature which are all private and closed-source. In this way, Wayverb is uniquely accurate, efficient, and accessible. Rather than presenting an entirely new simulation method, the Wayverb project surveys algorithms from the literature, employing those which are deemed most appropriate. It focuses on issues of practical implementation. In particular, for increased performance, Wayverb uses graphic hardware to accelerate calculations via parallelisation. Test data is presented to demonstrate accuracy. The Wayverb program demonstrates that the hybrid method is efficient enough to be viable in consumer software, but testing reveals that simulation results are not directly ready for production usage. The differing properties of the wave-based and geometric methods can result in different onset and decay times in the upper and lower regions of the output spectrum, which reduces the perceived quality of the output despite increased low-frequency accuracy. Avenues for further research are suggested in order to improve the quality and usability of the software

Diphthong Synthesis Using the Dynamic 3D Digital Waveguide Mesh

Articulatory speech synthesis has the potential to offer more natural sounding synthetic speech than established concatenative or parametric synthesis methods. Time-domain acoustic models are particularly suited to the dynamic nature of the speech signal, and recent work has demonstrated the potential of dynamic vocal tract models that accurately reproduce the vocal tract geometry. This paper presents a dynamic 3D digital waveguide mesh (DWM) vocal tract model, capable of movement to produce diphthongs. The technique is compared to existing dynamic 2D and static 3D DWM models, for both monophthongs and diphthongs. The results indicate that the proposed model provides improved formant accuracy over existing DWM vocal tract models. Furthermore, the computational requirements of the proposed method are significantly lower than those of comparable dynamic simulation techniques. This paper represents another step toward a fully functional articulatory vocal tract model which will lead to more natural speech synthesis systems for use across society

Numerical simulation of microwave heating of a target with temperature dependent electrical properties in a single-mode cavity

This dissertation extends the work done by Hue and Kriegsmann in 1998 on microwave heating of a ceramic sample in a single-mode waveguide cavity. In that work, they devised a method combining asymptotic and numerical techniques to speed up the computation of electromagnetic fields inside a high-Q cavity in the presence of low-loss target. In our problem, the dependence of the electrical conductivity on temperature increases the complexity of the problem. Because the electrical conductivity depends on temperature, the electromagnetic fields must be recomputed as the temperature varies. We then solve the coupled heat equation and Maxwell\u27s equations to determine the history and distribution of the temperature in the ceramic sample. This complication increases the overall computational effort required by several orders of magnitude. In their work, Hile and Kriegsmann used the established technique of solving the time-dependent Maxwell\u27s equations with the finite-difference time domain method (FDTD) until a time-harmonic steady state is obtained. Here we replace this technique with a more direct solution of a finite-difference approximation of the Helmholtz equation. The system of equations produced by this finite-difference approximation has a matrix that is large and non-Hermitian. However, we find that it may be splitted into the sum of a real symmetric matrix and a relatively low-rank matrix. The symmetric system represents the discretization of Helmholtz equation inside an empty and truncated waveguide; this system can be solved efficiently with the conjugate gradient method or fast Fourier transform. The low-rank matrix carries the information at the truncated boundaries of the waveguide and the properties of the sample. The rank of this matrix is approximately the sum of twice the number of grid spacings across waveguide and the number of grid points in the target. As a result of the splitting, we can handle this part of the problem by solving a system having as many unknowns as the rank of this matrix. With the above algorithmic innovations, substantial computational efficiencies have been obtained. We demonstrate the heating of a target having a temperature dependent electrical conductivity. Comparison with computations for constant electrical conductivity demonstrate significant difference in the heating histories. The computational complexity of our approach in comparison with that of using the FDTD solver favors the FDTD method when ultra-fine grids are used. However, in cases where grids are refined simply to reduce asymptotic truncation error, our method can retain its advantages by reducing truncation error through higher-order discretization of the Helmholtz operator