Room acoustic synthesis can be used in virtual reality (VR), augmented reality (AR) and gaming applications to enhance listeners' sense of immersion, realism and externalisation. A common approach is to use geometrical acoustics (GA) models to compute impulse responses at interactive speed, and fast convolution methods to apply said responses in real time. Alternatively, delay-network-based models are capable of modeling certain aspects of room acoustics, but with a significantly lower computational cost. In order to bridge the gap between these classes of models, recent work introduced delay network designs that approximate Acoustic Radiance Transfer (ART), a geometrical acoustics (GA) model that simulates the transfer of acoustic energy between discrete surface patches in an environment. This paper presents two key extensions of such designs. The first extension involves a new physically-based and stability-preserving design of the feedback matrices, enabling more accurate control of scattering and, more in general, of late reverberation properties. The second extension allows an arbitrary number of early reflections to be modeled with high accuracy, meaning the network can be scaled at will between computational cost and early reverberation precision. The proposed extensions are compared to the baseline ART-approximating delay network as well as two reference GA models. The evaluation is based on objective measures of perceptually-relevant features, including frequency-dependent reverberation times, echo density build-up, and early decay time. Results show how the proposed extensions result in a significant improvement over the baseline model, especially for the case of non-convex geometries or the case of unevenly distributed wall absorption, both scenarios of broad practical interest.

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.

In room acoustics simulation and virtualization applications, accurate wall termination is a perceptually crucial feature. It is particularly important in the setting of wave-based modeling of 3D spaces, using methods such as the finite difference time domain method or finite volume time domain method. In this paper, general locally reactive impedance boundary conditions are incorporated into a 3D finite volume time domain formulation, which may be specialized to the various types of finite difference time domain method under fitted boundary termination. Energy methods are used to determine stability conditions for general room geometries, under a large family of nontrivial wall impedances, for finite volume methods over unstructured grids. Simulation results are presented, highlighting in particular the need for unstructured or fitted cells at the room boundary in the case of the accurate simulation of frequency-dependent room mode decay times.

In the audio signal processing field, multiple IIR filters are required in many applications. As an example, equalizing a Wave Field Synthesis system requires massive filter processing in real time. Graphics Processing Units (GPUs) are well known for their potential in highly parallel data processing. Up to now, the use of the GPUs for implementing IIR filters has not been clearly tackled in audio processing because of its feedback loop that prevents its total parallelization. However, using the Parallel form of IIR filters, this feedback is reduced, since every single sample is computed in a parallel way. This paper analyzes the performance of multiple IIR filters using GPUs and compares it with a powerful multi-core computer. The proposed GPU implementation can run up to 1256 concurrent IIR filters of order 256th in real time, which means 321,536 total filter order, with a latency time of 0.72 ms (sampling frequency of 44.1 kHz). This demonstrates that GPUs are well suited for computing massive IIR filtering.

Finite difference solutions to the wave equation are simple and flexible modeling tools for approximating physical systems in audio and room acoustics. Each model is characterized by a matrix operator and the time-stepping solution by a sequence of powers of the matrix. Spectral decomposition of representative matrices provide some practical insight into solution behavior and in some cases stability. In addition to computed eigenvalue spectra, pseudospectra provide a description of numerical amplification due to rounding errors in floating point arithmetic. The matrix analysis also shows that certain boundary implementations in non-cuboid geometries can be unstable despite satisfying conditions derived from von Neumann and normal mode analyses.

Room acoustic simulation is the process of generating approximate solutions to either the linearized Euler equations or the scalar wave equation. As for the continuous equations, the discrete approximations of both are equivalent. The vector formulation is less efficient, but it can inform several unexploited features of the scalar formulation. This paper first demonstrates the equivalence of the two schemes and explores how the vector formulation may be integrated into the more efficient scalar formulation to produce local velocity estimates and velocity sources on the pressure grid.

Finite-difference time domain methods are commonly used for acoustics modeling of enclosed geometries. For large spaces and high frequencies, the computational requirements become prohibitive in practical use. Thus, geometric acoustics algorithms are used in those cases. The results of these two classes of algorithm can be combined to model the full acoustic response. To allow direct mixing of the results, the source strengths should be calibrated. This paper derives calibration factors for various finite-difference time domain methods. It is shown that the modelled acoustics responses can then be easily combined to synthesise wide-band hybrid responses.

Synthesizing the room impulse response (RIR) of an arbitrary enclosure may be performed using a number of alternative acoustic modeling methods, each with their own particular advantages and limitations. This article is concerned with obtaining a hybrid RIR derived from both wave and geometric-acoustics based methods, optimized for use across different regions of time or frequency. Consideration is given to how such RIRs can be matched across modeling domains in terms of both amplitude and boundary behavior and the approach is verified using a number of standardised case studies.

A single room impulse response can reveal information about the acoustics of a given space in both objective, and, when used for auralization, subjective terms. However, for additional spatial information, or more accurate and perceptually convincing auralization, multiple impulse responses are needed. Higher order Ambisonics is a robust means of capturing the spatial qualities of an acoustic space over multiple channels for decoding and rendering over many possible speaker layouts. A method for obtaining$N$th-order Ambisonic impulse responses from a room acoustic model, based on lower orders using differential microphone techniques is presented. This is tested using a third-order encoding of a 2-D finite difference time domain room acoustic simulation based on multiple circular arrays of receivers. Accurate channel directional profiles are obtained and results are verified in a series of listening tests comparing the localization of a sound source placed within the given simulation to the same source encoded directly. This generic encoding scheme can be applied to any room acoustic simulation technique where it is possible to obtain impulse responses across multiple receiver positions. Although the proposed method encompasses horizontal encoding only, it can also be applied directly in 3-D simulations where height information is not required in the final auralization.

The first artificial reverberation algorithms were proposed in the early 1960s, and new, improved algorithms are published regularly. These algorithms have been widely used in music production since the 1970s, and now find applications in new fields, such as game audio. This overview article provides a unified review of the various approaches to digital artificial reverberation. The three main categories have been delay networks, convolution-based algorithms, and physical room models. Delay-network and convolution techniques have been competing in popularity in the music technology field, and are often employed to produce a desired perceptual or artistic effect. In applications including virtual reality, predictive acoustic modeling, and computer-aided design of acoustic spaces, accuracy is desired, and physical models have been mainly used, although, due to their computational complexity, they are currently mainly used for simplified geometries or to generate reverberation impulse responses for use with a convolution method. With the increase of computing power, all these approaches will be available in real time. A recent trend in audio technology is the emulation of analog artificial reverberation units, such as spring reverberators, using signal processing algorithms. As a case study we present an improved parametric model for a spring reverberation unit.

We present an interactive sound propagation algorithm that can compute high orders of specular and diffuse reflections as well as edge diffractions in response to moving sound sources and a moving listener. Our formulation is based on a precomputed acoustic transfer operator, which we compactly represent using the Karhunen-Loeve transform. At runtime, we use a two-pass approach that combines acoustic radiance transfer with interactive ray tracing to compute early reflections as well as higher-order reflections and late reverberation. The overall approach allows accuracy to be traded off for improved performance at runtime, and has a low memory overhead. We demonstrate the performance of our algorithm on different scenarios, including an integration of our algorithm with Valve's Source game engine.

This paper presents a novel platform for interactive virtual room acoustics simulation and visualization. The platform is based on two autonomous modules: EVERTims for acoustic simulation and Audio2graphical for graphical rendering and interaction management. The system is a tool for acousticians and architects to understand better the acoustic properties of a closed space. Beside visualizing sound reflections, it allows navigation as well as geometrical properties modification of a given sound source and a listener.

In this paper, a simple family of explicit two-step finite difference methods for solving the classical equation of motion of a thin plate is examined. This family depends on several free parameters, and special attention is paid to the stability properties of these schemes, computational issues, and, in particular, the reduction of directional numerical dispersion. Numerical results, employing frequency warping techniques, are presented

A novel method for simulation of acoustic spaces, such as concert halls or listening rooms, using several 2-D digital waveguide mesh simulations is discussed. The advantages of this approach include reduced computational load, reduced memory usage, and simplified model structure in comparison to a 3-D waveguide mesh simulation. In approximating the modal frequencies of rooms, all the most important lowest modes get modeled, but some higher modes are missing. The proposed method is useful for finding low-frequency modes and for detecting changes in modal distribution when a sound source is moved, for example. As an acoustic visualization tool, the method is superior over a 3-D simulation in that it can isolate a certain layer of the acoustic wave field and it automatically hides waves that propagate in other directions and thus confuse the visualization

The digital waveguide mesh is a method for simulating wave propagation, for example, in an acoustic system. Research on the boundary conditions has been going on for years, but adequate solutions for absorbing boundaries have not yet been presented for the digital waveguide mesh. In this work, a new method for constructing absorbing boundaries for a two-dimensional (2-D) rectangular mesh is introduced. With the use of the proposed numerically optimized spatial filtering with an interpolated mesh structure, the reflection was diminished to under -25 dB at incidence angles |/spl theta/|/spl les/79.26/spl deg/ on a frequency band limited only at the very lowest and highest ends.

The digital waveguide mesh is a modeling technique suitable for simulation of wave propagation in an acoustic system. Artificial boundary conditions are constructed for the digital waveguide mesh. Absorbing boundary conditions are evaluated and a new method for adjusting the reflection coefficient at values 0/spl les/r/spl les/1 is introduced. The frequency dependent error level of this method is minimized by the use of a second-order FIR filter.

This paper describes a systematic approach to specification and compilation of different physical modeling schemes particularly for sound synthesis studies. First we formulate theoretically a unified way of constructing physical interaction models which include elements that use both wave variables and Kirchhoff variables. These elements can be applied to build 1D and multidimensional structures as well as lumped element models. In addition, typical signal processing algorithms are supported. A software environment (Block Compiler) has been developed, allowing for high-level object-based specification of physical models and their compilation to efficient code for execution.

Various interpolated three-dimensional (3-D) digital waveguide mesh algorithms are elaborated. We introduce an optimized technique that improves a formerly proposed trilinearly interpolated 3-D mesh and renders the mesh more homogeneous in different directions. Furthermore, various sparse versions of the interpolated mesh algorithm are investigated, which reduce the computational complexity at the expense of accuracy. Frequency-warping techniques are used to shift the frequencies of the output signal of the mesh in order to cancel the effect of dispersion error. The extensions improve the accuracy of 3-D digital waveguide mesh simulations enough so that in the future it can be used for acoustical simulations needed in the design of listening rooms, for example.

The goal of this paper is to give an overview of real-time room acoustic rendering. The approach is based on the source-medium-receiver model, in which we model sound sources, room acoustics, and a listener. The basic techniques for each of these are presented, but the main emphasis is on the room acoustic modeling and interactive auralization. As a case study we present the structure of the DIVA auralization system developed at the Helsinki University of Technology. In addition, we describe subjective evaluations made to our system. Finally, a discussion of some applications of virtual acoustics and their computational needs are given.

An interpolated 3-D digital waveguide mesh algorithm is elaborated. We introduce an optimized technique that improves a formerly proposed interpolated 3-D mesh and renders the 3-D mesh more homogeneous in different directions. Frequency-warping techniques are used to shift the frequencies of the output signal of the mesh in order to cancel the effect of dispersion error. The extensions improve the accuracy of 3-D digital waveguide mesh simulations enough so that in the future it can be used for acoustical simulations needed in the design of listening rooms, for example.

A multiwarping technique is introduced. The method is based on cascading frequency warping procedures and sample rate conversions. As a practical example, we show that with this new approach, the maximal frequency error of digital waveguide mesh simulations can be reduced by about 50%. This technique gives more degrees of freedom to attain a desired amount of nonlinear frequency shift still applying first-order allpass filters for processing finite-length digital impulse responses.

The digital waveguide mesh is an extension of the one-dimensional (1-D) digital waveguide technique. The mesh can be used for simulation of two- and three-dimensional (3-D) wave propagation in musical instruments and acoustic spaces. The original rectangular digital waveguide mesh algorithm suffers from direction-dependent dispersion. Alternative geometries, such as the triangular mesh, have been proposed previously to improve the performance of the mesh. In this paper, we show that the dispersion problem may be reduced using various other techniques. These methods include multidimensional interpolation, optimization of the point-spreading function, and frequency warping. We compare the accuracy and computational complexity of these techniques in the two-dimensional (2-D) case and conduct numerical simulations of a membrane. A rectangular mesh using second-order Lagrange interpolation can be implemented without multiplications, but its accuracy is worse than that of other enhanced structures. The most accurate technique in terms of the relative frequency error is the warped triangular mesh whose maximum error is 0.6%. The warped rectangular mesh with optimized weighting coefficients is not as exact, but still offers a 1.2% accuracy.

The digital waveguide mesh is an extension of the one-dimensional digital waveguide technique. The mesh is used for simulation of two- and three-dimensional wave propagation in musical instruments and acoustic spaces. The rectangular digital waveguide mesh algorithm suffers from direction-dependent dispersion. By using the interpolated mesh, nearly uniform wave propagation characteristics are obtained in all directions. In this paper we show how the dispersion error of the interpolated mesh can be reduced by frequency warping. By using this technique the bandwidth where the frequency accuracy is within 1% tolerance is more than doubled.

The digital waveguide mesh has been successfully used for simulation of two-dimensional (2-D) and three-dimensional (3-D) wave propagation in musical instruments and acoustic spaces. Nevertheless, digital waveguide mesh algorithms suffer from dispersion which increases with frequency. In this letter, we show how the dispersion error of the triangular digital waveguide mesh can be reduced by frequency warping. By using this technique, the worst-case dispersion error of 0.6% is obtained, whereas in the original triangular mesh it is about 6.5%.

The digital waveguide mesh is an extension of the one-dimensional digital waveguide technique. Waveguide meshes are used for simulation of two- and three-dimensional wave propagation in musical instruments and acoustic spaces. The original waveguide mesh algorithm suffers from direction-dependent dispersion. In this paper we show that this problem may be reduced by using an interpolated rectilinear mesh. In the analysis part we show the analytical solution for the wave propagation speed and numerical simulations of the magnitude response and phase speed in both the original and the interpolated two-dimensional waveguide mesh algorithms. We demonstrate by simulation that the wave propagation characteristics of the proposed interpolated waveguide mesh are independent of direction and thus the remaining errors caused by dispersion may be corrected with a postprocessor.