Jens Ahrens

An Analytical Approach to Sound Field Reproduction Using Circular and Spherical Loudspeaker Distributions

In this paper, we present the theoretical basics and implementation strategies for sound field reproduction using circular and spherical loudspeaker arrays. The presented approach can be seen as an analytical formulation of what is known as higher order Ambisonics. It relies on the assumption of a continuous distribution of secondary sources on which sampling is performed to yield the loudspeaker driving signals for real-world implementations. We present the theoretical derivation of the loudspeaker driving signals and investigate the properties of the actual reproduced wave field, whereby the focus lies on the consequences of the spatial discretization of the secondary source distribution.

Sound Field Reproduction Using Planar and Linear Arrays of Loudspeakers

In this paper, we consider physical reproduction of sound fields via planar and linear distributions of secondary sources (i.e., loudspeakers). The presented approach employs a formulation of the reproduction equation in spatial frequency domain which is explicitly solved for the secondary source driving signals. Wave field synthesis (WFS), the alternative formulation, can be shown to be equivalent under equal assumptions. Unlike the WFS formulation, the presented approach does not employ a far-field approximation when linear secondary source distributions are considered but provides exact results. We focus on the investigation of the spatial truncation and discretization of the secondary source distribution occurring in real-world implementations and present a rigorous analysis of evanescent and propagating components in the reproduced sound field.

Analytic Methods of Sound Field Synthesis

This book puts the focus on serving human listeners in the sound field synthesis although the approach can be also exploited in other applications such as underwater acoustics or ultrasonics. The author derives a fundamental formulation based on standard integral equations and the single-layer potential approach is identified as a useful tool in order to derive a general solution. He also proposes extensions to the single-layer potential approach which allow for a derivation of explicit solutions for circular, planar, and linear distributions of secondary sources. Based on above described formulation it is shown that the two established analytical approaches of Wave Field Synthesis and Near-field Compensated Higher Order Ambisonics constitute specific solutions to the general problem which are covered by the single-layer potential solution and its extensions.

Analytical driving functions for higher order Ambisonics

In this paper, we present the derivation and investigation of analytical expressions for the loudspeaker driving signals for higher order Ambisonics. The approach relies on the assumption of a continuous distribution of secondary sources on which sampling is performed to yield the actual loudspeaker signals for real-world implementations. For source-free volumes enclosed by the secondary source distribution, this formulation of Ambisonics leads to what is known as simple source approach. Since the simple source approach is theoretically well documented, we will depart from it and concentrate on the special case of a circular distribution of secondary point sources and derive analytical expressions for the driving signals. We furthermore derive a closed-form expression for the actual reproduced wave field for the circular secondary source distribution.

HRTF magnitude synthesis via sparse representation of anthropometric features

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 subjects anthropometric features w.r.t. the anthropometric features in the training set. The fundamental assumption is that the magnitudes of a given HRTF set can be described by the same sparse combination as the anthropometric data. Thus, we learn a sparse vector that represents the subjects anthropometric features as a linear superposition of the anthropometric features of a small subset of subjects from the training data. Then, we apply the same sparse vector directly on the HRTF tensor data. For evaluation purpose we use a new dataset, containing both anthropometric features and HRTFs. We compare the proposed sparse representation based approach with ridge regression and with the data of a manikin (which was designed based on average anthropometric data), and we simulate the best and the worst possible classifiers to select one of the HRTFs from the dataset. For instrumental evaluation we use log-spectral distortion. Experiments show that our sparse representation outperforms all other evaluated techniques, and that the synthesized HRTFs are almost as good as the best possible HRTF classifier.

Spatial perception of sound fields recorded by spherical microphone arrays with varying spatial resolution

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 spherical harmonics domain. In spite of these developments, a clear relation between sound fields recorded by spherical microphone arrays and their perception with a re-synthesis system has not yet been established, although some relation to scalar measures of spatial perception was recently presented. This paper presents an experimental study of spatial sound perception with the use of a spherical microphone array for sound recording and headphone-based binaural sound synthesis. Sound field analysis and processing is performed in the spherical harmonics domain with the use of head-related transfer functions and simulated enclosed sound fields. The effect of several factors, such as spherical harmonics order, frequency bandwidth, and spatial sampling, are investigated by applying the repertory grid technique to the results of the experiment, forming a clearer relation between sound-field capture with a spherical microphone array and its perception using binaural synthesis regarding space, frequency, and additional artifacts. The experimental study clearly shows that a source will be perceived more spatially sharp and more externalized when represented by a binaural stimuli reconstructed with a higher spherical harmonics order. This effect is apparent from low spherical harmonics orders. Spatial aliasing, as a result of sound field capturing with a finite number of microphones, introduces unpleasant artifacts which increased with the degree of aliasing error.

Wave field synthesis of a sound field described by spherical harmonics expansion coefficients

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 arrays. Such recorded sound fields are essentially represented by the coefficients of the underlying surface spherical harmonics expansion. A sound field described by such coefficients cannot be straightforwardly synthesized in WFS. This is a consequence of the fact that, unlike in NFC-HOA, it is critical in WFS to carefully select those loudspeakers that contribute to the synthesis of a given sound source in a sound field under consideration. In order to enable such a secondary source selection, it is proposed to employ the well-known concept of decomposing the sound field under consideration into a continuum of plane waves, for which the secondary source selection is straightforward. The plane wave representation is projected onto the horizontal plane and a closed form expression of the secondary source driving signals for horizontal WFS systems of arbitrary convex shape is derived.

Object-based audio reproduction and the audio scene description format

The introduction of new techniques for audio reproduction such as HRTF-based technology, wave field synthesis and higher-order Ambisonics is accompanied by a paradigm shift from channel-based to object-based transmission and storage of spatial audio. Not only is the separate coding of source signal and source location more efficient considering the number of channels used for reproduction by large loudspeaker arrays, it also opens up new options for a user-controlled interactive sound field design. This article describes the need for a common exchange format for object-based audio scenes, reviews some existing formats with potential to meet some of the requirements and finally introduces a new format called Audio Scene Description Format (ASDF) and presents the SoundScape Renderer, an audio reproduction software which implements a draft version of the ASDF.

Reproduction of focused sources by the spectral division method

Sound reproduction methods based on the physical resynthesis of a desired field using loudspeaker arrays are well-established nowadays. Their physical basis allows to resynthesize almost any desired wave field, even the field of sound sources positioned in between the loudspeakers and the listener. Such sources are known as focused sources. This paper will present a novel approach to the reproduction of focused sources with linear loudspeaker arrays. Its formulation is based on a representation of the respective fields in the spatio-temporal frequency domain. The derivation of the loudspeaker driving function is discussed, as well as a number of practical limits, the role of evanescent contributions and the connections to other established techniques.

The multi-touch SoundScape renderer

In this paper, we introduce a direct manipulation tabletop multi-touch user interface for spatial audio scenes. Although spatial audio rendering exists for several decades now, mass market applications have not been developed and the user interfaces still address a small group of expert users. We implemented an easy-to-use direct manipulation interface for multiple users, taking full advantage of the object-based audio rendering mode. Two versions of the user interface have been developed to explore variations in information architecture and will be evaluated in user tests.