Lauri Savioja

The room acoustic rendering equation

An integral equation generalizing a variety of known geometrical room acoustics modeling algorithms is presented. The formulation of the room acoustic rendering equation is adopted from computer graphics. Based on the room acoustic rendering equation, an acoustic radiance transfer method, which can handle both diffuse and nondiffuse reflections, is derived. In a case study, the method is used to predict several acoustic parameters of a room model. The results are compared to measured data of the actual room and to the results given by other acoustics prediction software. It is concluded that the method can predict most acoustic parameters reliably and provides results as accurate as current commercial room acoustic prediction software. Although the presented acoustic radiance transfer method relies on geometrical acoustics, it can be extended to model diffraction and transmission through materials in future.

Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques

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.

Creating interactive virtual auditory environments

We survey sound rendering techniques by comparing them to visual image rendering and describe several approaches for performing sound rendering in virtual auditory environments.

Fifty Years of Artificial Reverberation

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.

Interpolated rectangular 3-D digital waveguide mesh algorithms with frequency warping

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.

Modeling of reflections and air absorption in acoustical spaces a digital filter design approach

A method is presented for modeling sound propagation in rooms using a signal processing approach. Low order digital filters are designed to match to sound propagation transfer functions calculated from boundary material and air absorption data. The technique is applied to low frequency, finite difference time domain (FDTD) simulation of room acoustics and to real-time image-source based virtual acoustics.

Overview of geometrical room acoustic modeling techniques

Computerized room acoustics modeling has been practiced for almost 50 years up to date. These modeling techniques play an important role in room acoustic design nowadays, often including auralization, but can also help in the construction of virtual environments for such applications as computer games, cognitive research, and training. This overview describes the main principles, landmarks in the development, and state-of-the-art for techniques that are based on geometrical acoustics principles. A focus is given to their capabilities to model the different aspects of sound propagation: specular vs diffuse reflections, and diffraction.

Engaging concert hall acoustics is made up of temporal envelope preserving reflections

Strong, exciting, and engaging sound is perceived in the best concert halls. Here, it is shown that wideband early reflections that preserve the temporal envelope of sound contribute to the clear and open acoustics with strong bass. Such reflections are fused with the direct sound due to the precedence effect. In contrast, reflections that distort the temporal envelope render the sound weak and muddy because they partially break down the precedence. The presented findings are based on the earlier psychoacoustics research, and confirmed by a perceptual evaluation with six simulated concert halls that have same monaural room acoustical parameter values according to ISO3382-1.

Geometry reduction in room acoustics modeling

The complexity of a room model affects to the computational resources required to model its acoustics by means of geometrical acoustics modeling methods. Thus, a method for reducing the geometry of the room models is presented for static room geometries. The topology of the model is simplified in a process where the model is first decomposed into a volumetric structure. The surface is reconstructed by utilizing this structure, and subsequently simplified by merging coplanar regions. The results of the method are verified by extracting room acoustical attributes from the original and reduced models with the ODEON room acoustics prediction software. It is shown that the most important acoustic properties have been preserved, even with relatively high reduction rates.

Frequency domain acoustic radiance transfer for real-time auralization

A method for modeling room acoustics and auralizing the results in real time with a moving listener is presented. The acoustics modeling is based on the acoustic radiance transfer technique which is capable of modeling arbitrary reflection properties of different materials. The novel idea of implementing this technique in frequency domain allows modeling of all frequencies at once as the time domain technique requires separate runs for each frequency band. Since the auralization of the results requires scaling, adding, and delaying responses as well as convolving them with head-related impulse responses, the massive parallel computation capacity of modern graphics hardware is utilized. Thus, realistic interactive walkthroughs are possible in typical room models with a stationary source.