Spatial Acoustic Signal Processing

A sound field on a line or in a plane has an effectively limited spatial bandwidth determined by the temporal frequency. Similar can be said for sound fields from far-field sources when analyzed on circular and spherical apertures. Namely, for a given frequency and aperture size, a sound field is effectively composed of a finite number of circular or spherical harmonic components. Based on these two observations, it follows that if adequately sampled, sound fields can be represented and manipulated in a digital domain with negligible loss of information. The optimal sampling surface depends on the problem geometry, and the set of sampling points needs to be in accordance with the Nyquist criterion relative to the mentioned effective sound field bandwidth. In this thesis, we address the problems of sound field capture and reproduction from a practical perspective. More specifically, we present approaches that do not depend on acoustical models, but rely instead on obtaining an acoustic MIMO channel between transducers (microphones or loudspeakers) and a set of sampling (or control) points. Subsequently, sound field capture and reproduction are formulated as constrained optimization problems in a spatially discrete domain and solved using conventional numerical optimization tools. The first part of the thesis deals with spatial sound capture. We present a framework for analyzing and designing differential microphone arrays based on spatiotemporal sound field gradients. We also show how to record two- and three-dimensional sound fields with differential, circular, and spherical microphone arrays. Finally, we use the mentioned discrete optimization for computing filters for directional and sound field microphone arrays. In the second part of the thesis, we focus on spatial sound reproduction. We first present a design of a baffled loudspeaker array for reproducing sound with high directivity over a wide frequency range, which combines beamforming at low, and scattering from a rigid baffle at high frequencies. We next present Sound Field Reconstruction (SFR), which is an approach for optimally reproducing a desired sound field in a wide listening area by inverting a discrete, MIMO acoustic channel. In the end, we propose a single- and multi-channel low-frequency room equalization method, formulated as a discrete constrained optimization problem, with constraints designed to prevent excessive equalization filter gains, localization bias, and temporal distortions in the form of pre- and post-echos.

Design of a Compact Cylindrical Loudspeaker Array for Spatial Sound Reproduction

Christof Faller, Mihailo Kolundzija, Martin Vetterli

Building acoustic beamformers is a problem whose solution is hindered by the wide-band nature of audible sound. In order to achieve a consistent directional response over a wide range of frequencies, a conventional acoustic beamformer needs a high number of discrete loudspeakers and be large enough to achieve a desired low-frequency performance. The acoustic beamformer design described in this paper uses measurement-based optimized beamforming for loudspeakers mounted on a rigid cylindrical baffle. Super-directional beamforming enables achieving desired directivity with multiple loudspeakers at low frequencies. High frequencies are reproduced with a single loudspeaker, whose highly directional reproduction---due to the cylindrical baffle---matches the design goals. In addition to the beamformer filter design procedure, it is shown how such loudspeaker array can be used for spatial sound reproduction.

2011

A Universal Sampling Method for Reconstructing Signals with Simple Fourier Transforms

Mikhail Kapralov, Amir Zandieh

Reconstructing continuous signals based on a small number of discrete samples is a fundamental problem across science and engineering. We are often interested in signals with "simple" Fourier structure - e.g., those involving frequencies within a bounded range, a small number of frequencies, or a few blocks of frequencies i.e., bandlimited, sparse, and multiband signals, respectively. More broadly, any prior knowledge on a signal's Fourier power spectrum can constrain its complexity. Intuitively, signals with more highly constrained Fourier structure require fewer samples to reconstruct. We formalize this intuition by showing that, roughly, a continuous signal from a given class can be approximately reconstructed using a number of samples proportional to the statistical dimension of the allowed power spectrum of that class. We prove that, in nearly all settings, this natural measure tightly characterizes the sample complexity of signal reconstruction. Surprisingly, we also show that, up to log factors, a universal non-uniform sampling strategy can achieve this optimal complexity for any class of signals. We present an efficient and general algorithm for recovering a signal from the samples taken. For bandlimited and sparse signals, our method matches the state-of-the-art, while providing the the first computationally and sample efficient solution to a broader range of problems, including multiband signal reconstruction and Gaussian process regression tasks in one dimension. Our work is based on a novel connection between randomized linear algebra and the problem of reconstructing signals with constrained Fourier structure. We extend tools based on statistical leverage score sampling and column-based matrix reconstruction to the approximation of continuous linear operators that arise in the signal reconstruction problem. We believe these extensions are of independent interest and serve as a foundation for tackling a broad range of continuous time problems using randomized methods.

ASSOC COMPUTING MACHINERY2019

Sound Field Reconstruction in a room through Sparse Recovery and its application in Room Modal Equalization

Vu Thach Pham

The acoustics of a room often refer to the quality of the room in terms of sound recording as well as sound reproduction. At low frequencies, where the wavelengths are of the same order of magnitude with the dimensions of the room, due to the standing waves phenomena, room modes are formed which can give rise to multiple irregularities and eventually damage the listening experience. In order to effectively address the problem at these frequencies, a thorough knowledge of the sound field in the room is often required. Through numerical studies, the sound field in the room could be simulated based on an FEM room model which would result in certain differences when comparing to the actual situation. On the other hand, the traditional experimental sampling of the sound field in a room often results in an impractical number of microphones.This thesis focuses on the development of a sound field reconstruction framework that makes use of certain sparse representation and recovery algorithm to reconstruct the sound field of the room at low frequencies using a limited set of microphones. The reconstruction framework is then tested under different conditions and scenarios to prove its validity. Once the performance of the framework has been validated through both simulation and actual measurements, the reconstruction framework is investigated in detail regarding its application in the field of active modal equalization. These active absorption methods are of high interest in the field of modal equalization due to the fact that passive absorption method at low frequencies are more often than not ineffective. The reconstruction framework is then used to first assess the spatial performance of the active electroacoustic absorbers which consists of a current-driven system of loudspeakers in enclosures that aims to dampen room modes by achieving optimal target impedance in front of the loudspeaker membranes. In addition, a more complex applications of the reconstruction framework in which its reconstructed sound field can be used to fine tune the control parameters of the active absorbers is also investigated. The research shows promising results in both application of the reconstruction frameworks and open doors to further development in both the field of sound field reconstruction as well as room modes equalization.