Jens Ahrens

Chalmers University of Technology · Department of Civil and Environmental Engineering

Six-degrees-of-freedom rendering of an acoustic environment can be achieved by interpolating a set of measured spatial room impulse responses (SRIRs). However, the involved measurement effort and computational expense are high. This work compares novel ways of extrapolating a single measured SRIR to a target position. The novel extrapolation techni...

Psychoacoustic experiments have shown that directional properties of, in particular, the direct sound, salient reflections, and the late reverberation of an acoustic room response can have a distinct influence on the auditory perception of a given room. Spatial room impulse responses (SRIRs) capture those properties and thus are used for direction-...

The domain of spatial audio comprises methods for capturing, processing, and reproducing audio content that contains spatial information. Data-based methods are those that operate directly on the spatial information carried by audio signals. This is in contrast to model-based methods, which impose spatial information from, for example, metadata lik...

The present document reviews the mathematics behind binaural rendering of sound fields that are available as spherical harmonic expansion coefficients. This process is also known as binaural ambisonic decoding. We highlight that the details entail some amount peculiarity so that one has to be well aware of the precise definitions that are chosen fo...

Additive noise produced by the recording hardware will contribute to streamed signals from spherical microphone arrays under practical conditions. For the application of binaural reproduction and under the assumption that the noise is uncorrelated between the array channels, the spectral properties and the overall level of the rendered noise in the...

We propose a method for the decomposition of measured directional room impulse responses (DRIRs) into prominent reflections and a residual. The method comprises obtaining a fingerprint of the time-frequency signal that a given reflection carries, imposing this time-frequency fingerprint on a plane-wave prototype that exhibits the same propagation d...

Spherical microphone array (SMA) recordings are particularly suited for dynamic binaural rendering as the microphone signals can be decomposed into a spherical harmonic (SH) representation that can be freely rotated to match the head orientation of the listener. The rendering of such SMA recordings is a non-trivial task as the SH signals are impair...

We recently presented a method for obtaining a spherical harmonic representation of a sound field based on microphones along the equator of a rigid spherical object that ideally has a size similar to that of a human head. We refer to this setup as equatorial microphone array. Even more recently, we presented an extension of this method that allows...

Find a pdf here: http://www.soundfieldsynthesis.org/wp-content/uploads/pubs/Ahrens_etal_JASA2021.pdf We present a method for computing a spherical harmonic representation of a sound field based on observations of the sound pressure along the equator of a rigid spherical scatterer. Our proposed solution assumes that the captured sound field is heig...

All acoustic sources are of finite spatial extent. In volumetric wave-based simulation approaches (including, e.g., the finite difference time domain method among many others), a direct approach is to represent such continuous source distributions in terms of a collection of point like sources at grid locations. Such a representation requires inter...

Spherical microphone arrays are used to capture spatial sound fields, which can then be rendered via headphones. Insight into perceptual properties of sensor self-noise is valuable in the design and construction process of such arrays. We use the Real-Time Spherical Array Renderer (ReTiSAR) to analyze the frequency-dependent white-noise-gain, i.e....

The measurement of directivity for sound sources that are not electroacoustic transducers is fundamentally limited because the source cannot be driven with arbitrary signals. A consequence is that directivity can only be measured at a sparse set of frequencies—for example, at the stable partial oscillations of a steady tone played by a musical inst...

This paper presents a perceptual evaluation of numerical dispersion in free-field headphone-based head-tracked binaural auralizations of finite difference time domain (FDTD) simulations. The simulated pressure, captured by virtual volumetric receiver arrays, is used to perform a spherical harmonics decomposition of the sound field and generate bina...

Employing a finite number of discrete microphones, instead of a continuous distribution according to theory, reduces the physical accuracy of sound field representations captured by a spherical microphone array. For a binaural reproduction of the sound field, a number of approaches have been proposed in the literature to mitigate the perceptual imp...

Spherical microphone arrays (SMAs) are widely used to capture spatial sound fields that can then be rendered in various ways as a virtual acoustic environment (VAE) including head-phone-based binaural synthesis. Several practical limitations have a significant impact on the fidelity of the rendered VAE. The finite number of microphones of SMAs lead...

Spherical microphone arrays are used to capture spatial sound fields, which can then be rendered via headphones. We use the Real-Time Spherical Array Renderer (ReTiSAR) to analyze and auralize the propagation of sensor self-noise through the processing pipeline. An instrumental evaluation confirms a strong global influence of different array and re...

We recently presented ReTiSAR, a framework for binaural rendering of spherical microphone array data in real-time. The array signals and the employed head-related transfer functions are processed in the spherical harmonics domain to compute the resulting ear signals and virtually place a listener into the captured sound field. In this contribution,...

The modeling of source directivity is a problem of longstanding interest in virtual acoustics and auralisation. This remains the case for newer time domain volumetric wave-based approaches to simulation such as the finite difference time domain (FDTD) method. In this article, a spatio-temporal model of acoustic wave propagation, including a source...

Time-domain wave-based simulation approaches such as the finite difference time domain (FDTD) method allow for a complete solution to the problem of virtual acoustics over the entire frequency range, in contrast with the methods of geometric acoustics which are valid in the limit of high frequencies. They also allow for flexible modelling of source...

A listening experiment is presented in which subjects rated the perceived differences in terms of spaciousness and timbre between a headphone-based headtracked dummy head auralization of a sound source in different rooms and a headphone-based headtracked auralization of a spherical microphone array recording of the same scenario. The underlying aur...

We present ReTiSAR (Real-Time Spherical Array Renderer), an open-source implementation of real-time binaural rendering of signals obtained from spherical microphone arrays. The implementation was performed in Python and bases on the previously published SOFiA toolbox as well as on sound_field_analysis-py. We can confirm that Python together with th...

We previously presented an implementation of a complete processing pipeline for the rendering of high-order spherical microphone array signals based on impulse responses in the Python package `sound_field_analysis-py`. Although the resulting ear impulse responses can be computed for different head orientations so that head tracking can be applied u...

Many approaches for the capture and auralization of real acoustic spaces have been proposed over the past century. Limited spatial resolution on the capture side has typically been the factor that caused compromises in the achievable authenticity of the auralization. Recent advancements in the field of microphone arrays provide new perspective part...

Acoustical levitation is an area with many applications ranging from medical drug delivery to micro-particle sorting. An application which has gained attention recently is the creation of volumetric displays by using small levitating objects. Advances in inexpensive ultrasonic phased arrays have increased the availability of dynamically controllabl...

Ever since the invention of technology to capture and playback audio recordings, researchers and practitioners have been investigating ways to capture are re-create the sound of acoustic spaces1,2. New waves of enthusiasm tended to break out with every milestone in the development of new hardware. Historic reports on demonstrations of live-versus-r...

Microphone arrays can capture the physical structure of a sound field. They are therefore potentially suited to capture and preserve the sound of acoustic spaces within given physical limitations that are determined by the construction of the array. Especially spherical microphone arrays have received considerable attention in this context. Superpo...

Four of the nine big Technical Universities in Germany, together with Chalmers University of Technology in Sweden, have developed a new Massive Open Online Course (MOOC) on the subject of Communication Acoustics. The idea is to foster education on the late Bachelor or early Master level by joining the expertise available at individual universities...

Local sound field synthesis allows for synthesizing a given desired sound field inside a limited target region such that the field is free of considerable spatial aliasing artifacts. Spatial aliasing artifacts are a consequence of overlaps due to unavoidable repetitions of the space-spectral coefficients of the secondary source driving function. We...

The Sound Field Synthesis Toolbox (SFS) for Matlab/Octave gives you the possibility to play around with sound field synthesis methods like Wave Field Synthesis (WFS) or near-field compensated Higher Order Ambisonics (NFC-HOA). There are functions to simulate monochromatic sound fields for different secondary source (loudspeaker) setups, time snapsh...

In this paper, we present and validate a freely available MATLAB Toolbox for imposing speech signal impairments similar to those occurring in real-world telecommunication systems. The purpose of the toolbox is to facilitate research on the perception of different dimensions of speech quality and their relation to technical system properties. In tha...

Massive multi-channel auralization approaches like Wave Field Synthesis and Higher Order Ambisonics experienced a pronounced hype in the late 2000s during which the primary research goal was maximizing the physical accuracy of the synthetic sound fields that they create. The hype eventually faded as the achievable advancements turned out to be limi...

Sound field synthesis has been pursued as a promising approach for spatial audio reproduction for large listening areas. Research is typically performed on small and mid-size systems. An increasing number of systems of cinema size and larger exist, which have shown to exhibit properties that cannot be observed with smaller setups. In particular, pr...

We propose a method for the synthesis of the magnitudes of Head-related Transfer Functions (HRTFs) using a sparse representation of anthropometric features. Our approach treats the HRTF synthesis problem as finding a sparse representation of the subject’s anthropometric features w.r.t. the anthropometric features in the training set. The fundamenta...

Spherical microphone and circular microphone arrays are useful for sampling sound fields that may be resynthesized with loudspeaker arrays. Spherical microphone arrays are desirable because of their ability to capture three-dimensional sound fields, however it is often more practical to construct loudspeaker arrays in the form of a closed circle lo...

Practical implementations of sound field synthesis evoke considerable artifacts that have to be considered in the creation of artificial reverberation. The most prominent artifact is spatial aliasing, which manifests itself as additional wave fronts that follow the desired synthetic wave front in time. These additional wave fronts propagate into di...

The Spectral Division Method is an analytic approach for sound field synthesis that determines the loudspeaker driving function in the wavenumber domain. Compact expressions for the driving function in time-frequency domain or in time domain can only be determined for a low number of special cases. Generally, the involved spatial Fourier transforms...

We propose the concept of gentle acoustic crosstalk cancelation, which aims at reducing the crosstalk between a loudspeaker and the listener's contralateral ear instead of eliminating it completely as aggressive methods intend to do. The expected benefit is higher robustness and a tendency to collapse less unpleasantly. The proposed method employs...

The area of sound field synthesis has significantly advanced in the past decade, facilitated by the development of high-quality sound-field capturing and re-synthesis systems. Spherical microphone arrays are among the most recently developed systems for sound field capturing, enabling processing and analysis of three-dimensional sound fields in the...

Head-related transfer functions (HRTFs) represent the acoustic transfer function from a sound source at a given location to the ear drums of a human. They are typically measured from discrete source positions at a constant distance. Spherical harmonics decompositions have been shown to provide a flexible representation of HRTFs. Practical constrain...

The design process for time-invariant acoustic beamformers often assumes that the microphones have an omnidirectional directivity pattern, a flat frequency response in the range of interest, and a 2D environment in which wavefronts propagate as a function of azimuth angle only. In this paper we investigate those cases in which one or more of these...

The theory of sound field synthesis methods like Wave Field Synthesis (WFS) and Near-field Compensated Higher Order Ambisonics (NFC-HOA) may be formulated based on the assumption of continuous distributions of secondary sources that enclose the receiver area in the general case. In practice, a finite number of discrete loudspeakers is used, which c...

The design of time-invariant beamformers is often posed as an optimization problem using practical design constraints. In many scenarios it is sufficient to assume that the microphones have an omnidirectional directivity pattern, a flat frequency response in the range of interest, and a 2D environment in which wavefronts propagate as a function of...

Near-field compensated higher order Ambisonics (NFC-HOA) and wave field synthesis (WFS) constitute the two best-known analytic sound field synthesis methods. While WFS is typically used for the synthesis of virtual sound scenes, NFC-HOA is typically employed in order to synthesize sound fields that have been captured with appropriate microphone arr...

The synthesis of a captured sound field with preservation of its perceptual properties is called auralization. Data-based Wave Field Synthesis (WFS) auralization makes use of a set of measured impulse responses along an array of microphone positions. However, a considerable array size must be employed for having an appropriate angular resolution. I...

Based on the theory developed in the previous chapters, applications of sound field synthesis are presented that allow, e.g., for the synthesis of virtual sound sources with complex radiation properties, focused sources, spatially extended sources, moving sources, and alike. Other practical aspects like the storage and transmission of content for s...

This chapter presents a number of analytic solutions to the problem of sound field synthesis in three and 2.5 dimensions, whereby continuous distributions of secondary sources are assumed. A focus lies on the explicit solution of the synthesis equation, which provides a perfect solution for enclosing secondary source distributions. The explicit sol...

The continuous secondary source distributions treated in the previous chapter can not be implemented with today’s available technology. Continuous distributions have to be approximated by a finite number of discrete loudspeakers. The analogies of this spatial discretization to the discretization continuous time signals are outlined, based on which...

The present chapter outlines the mathematical and physical tools that are employed in the subsequent chapters. It is not written in a tutorial style but serves rather as a reference. The wave equation and its solutions in Cartesian as well as in spherical coordinates are introduced. Then, a number of useful representations of sound fields such as t...

The SoundScape Renderer is a versatile software framework for real-time spatial audio rendering. The modular system architecture allows the use of arbitrary rendering methods. Three rendering modules are currently implemented: Wave Field Synthesis, Vector Base Amplitude Panning and Binaural Rendering. After a description of the software architectur...

Higher order Ambisonics (HOA) is an approach to the physical (re-)synthesis of a given wave field. It is based on the orthogonal expansion of the involved wave fields formulated for interior problems. This implies that HOA is per se only capable of recreating the wave field generated by events outside the listening area. When a virtual source is in...

Near-field Compensated Higher Order Ambisonics (NFC-HOA) is an approach to the physical synthesis of sound fields. The typical interpretation of the modern NFC-HOA approach is that the sound field to be synthesized and the spatial transfer function of the employed loudspeakers are expanded into series of spherical harmonics in order to determine th...

The area of sound field synthesis has significantly advanced in the past decade, facilitated by the development of high-quality sound-field capturing and re-synthesis systems. Spherical microphone arrays are among the most recently developed systems for sound field capturing, enabling processing and analysis of three-dimensional sound fields in the...

The present Matlab scripts accompany the book "Analytic Methods of Sound Field Synthesis" by Jens Ahrens. Usage instructions can be found here: http://www.soundfieldsynthesis.org/matlab/

An approach to the synthesis of moving virtual sound sources with complex radiation properties in wave field synthesis is presented. The approach exploits the fact that any stationary sound source of finite spatial extent radiates spherical waves at sufficient distance. The angular dependency of the radiation properties of the source under consider...

Near-field compensated higher order Ambisonics is a sound field synthesis technique which is based upon a mathematical representation in terms of surface spherical harmonics. The generation of loudspeaker driving signals using digital signal processing is a numerically challenging task due to the involved special functions. This paper presents an e...

Virtual environments which are based on binaural sound reproduction require datasets of head-related transfer functions (HRTFs). Ideally, these HRTFs are available for every possible position of a virtual sound source. However, in order to reduce measurement efforts, such datasets are typically only available for various source directions but only...

Methods like Wave Field Synthesis aim at the synthesis of a given desired sound� eld over a large receiver area. Practical limitations lead to considerable artifacts commonly referred to as spatial aliasing. Above a given frequency these artifacts are apparent anywhere in the receiver area when linear arrays of secondary sources are considered. Th...

Head-related impulse responses (HRIRs), which are measured from an acoustic source to the left and right ear, characterize the acoustic properties of the outer ear. Due to the involved measurement effort, HRIRs are typically available only for source positions on a circle or surface of a sphere. Range extrapolation techniques aim at calculating HRI...

We present physical models for the sound field radiated by plates of finite size and spheres vibrating in higher modes. The intention is obtaining a model that allows for controlling the perceived spatial extent of a virtual sound source in model-based sound field synthesis. Analytical expressions for the radiated sound fields are derived and simul...