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.

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.

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 like the intended position of a source onto signals that are otherwise free of spatial information. Signal processing has traditionally been at the core of spatial audio systems, and it continues to play a very important role. The irruption of deep learning in many closely related fields has put the focus on the potential of learning-based approaches for the development of data-based spatial audio applications. This article reviews the most important application domains of data-based spatial audio including well-established methods that employ conventional signal processing while paying special attention to the most recent achievements that make use of machine learning. Our review is organized based on the topology of the spatial audio pipeline that consist in capture, processing/manipulation, and reproduction. The literature on the three stages of the pipeline is discussed, as well as on the spatial audio representations that are used to transmit the content between them, highlighting the key references and elaborating on the underlying concepts. We reflect on the literature based on a juxtaposition of the prerequisites that made machine learning successful in domains other than spatial audio with those that are found in the domain of spatial audio as of today. Based on this, we identify routes that may facilitate future advancement.

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 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 subject's 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.