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Detection, Estimation, and Modulation Theory

Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

Analysis and design of spherical microphone arrays

The theory of recording and reproduction of three-dimensional sound fields based on spherical harmonics is reviewed and extended. Free-field, sphere, and general recording arrays are reviewed, and the mode-matching and simple source approaches to sound reproduction in anechoic environments are discussed. Both methods avoid the need for both monopole and dipole loudspeakers—as required by the Kirchhoff–Helmholtz integral. An error analysis is presented and simulation examples are given. It is also shown that the theory can be extended to sound reproduction in reverberant environments.

/pdf/three-dimensional-surround-sound-systems-based-on-spherical-gts6rffrmw.pdf

Three-Dimensional Surround Sound Systems Based on Spherical Harmonics

Speech enhancement and separation are core problems in audio signal processing, with commercial applications in devices as diverse as mobile phones, conference call systems, hands-free systems, or hearing aids. In addition, they are crucial preprocessing steps for noise-robust automatic speech and speaker recognition. Many devices now have two to eight microphones. The enhancement and separation capabilities offered by these multichannel interfaces are usually greater than those of single-channel interfaces. Research in speech enhancement and separation has followed two convergent paths, starting with microphone array processing and blind source separation, respectively. These communities are now strongly interrelated and routinely borrow ideas from each other. Yet, a comprehensive overview of the common foundations and the differences between these approaches is lacking at present. In this paper, we propose to fill this gap by analyzing a large number of established and recent techniques according to four transverse axes: 1 the acoustic impulse response model, 2 the spatial filter design criterion, 3 the parameter estimation algorithm, and 4 optional postfiltering. We conclude this overview paper by providing a list of software and data resources and by discussing perspectives and future trends in the field.

/pdf/a-consolidated-perspective-on-multimicrophone-speech-qnbaqxmtvq.pdf

A Consolidated Perspective on Multimicrophone Speech Enhancement and Source Separation

Spherical microphone arrays have been recently studied for sound analysis and sound recordings, which have the advantage of spherical symmetry facilitating three-dimensional analysis. This paper complements the recent microphone array design studies by presenting a theoretical analysis of plane-wave decomposition given the sound pressure on a sphere. The analysis uses the spherical Fourier transform and the spherical convolution, where it is shown that the amplitudes of the incident plane waves can be calculated as a spherical convolution between the pressure on the sphere and another function which depends on frequency and the sphere radius. The spatial resolution of plane-wave decomposition given limited bandwidth in the spherical Fourier domain is formulated, and ways to improve the computation efficiency of plane-wave decomposition are introduced. The paper concludes with a simulation example of plane-wave decomposition.

/pdf/plane-wave-decomposition-of-the-sound-field-on-a-sphere-by-18uxxijpmr.pdf

Plane-wave decomposition of the sound field on a sphere by spherical convolution

This paper describes a beamforming microphone array consisting of pressure microphones that are mounted on the surface of a rigid sphere. The beamformer is based on a spherical harmonic decomposition of the soundfield. We show that this allows a simple and computationally effective, yet flexible beamformer structure. The look-direction can be steered to any direction in 3-D space without changing the beampattern. In general the number of sensors and their location is quite arbitrary as long as they hold a certain orthogonality constraint that we derived. For a practical example we chose a spherical array with 32 elements. The microphones are located at the center of the faces of a truncated icosahedron. The radius of the sphere is 5 cm. With this setup we can achieve a Directivity Index of 12 dB and higher. The operating frequency range is from 100 Hz to 5 kHz.

A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield

In one embodiment, a directional microphone array having (at least) two microphones generates forward and backward cardioid signals from two (e.g., omnidirectional) microphone signals. An adaptation factor is applied to the backward cardioid signal, and the resulting adjusted backward cardioid signal is subtracted from the forward cardioid signal to generate a (first-order) output audio signal corresponding to a beampattern having no nulls for negative values of the adaptation factor. After low-pass filtering, spatial noise suppression can be applied to the output audio signal. Microphone arrays having one (or more) additional microphones can be designed to generate second- (or higher-) order output audio signals.

Noise-reducing directional microphone array

A microphone array-based audio system that supports representations of auditory scenes using second-order (or higher) harmonic expansions based on the audio signals generated by the microphone array. In one embodiment, a plurality of audio sensors are mounted on the surface of an acoustically rigid sphere. The number and location of the audio sensors on the sphere are designed to enable the audio signals generated by those sensors to be decomposed into a set of eigenbeams having at least one eigenbeam of order two (or higher). Beamforming (e.g., steering, weighting, and summing) can then be applied to the resulting eigenbeam outputs to generate one or more channels of audio signals that can be utilized to accurately render an auditory scene. Alternative embodiments include using shapes other than spheres, using acoustically soft spheres and/or positioning audio sensors in two or more concentric patterns.

Audio system based on at least second-order eigenbeams

With the recent widespread availability of inexpensive DVD players and home theater systems, surround sound has become a mainstream consumer technology. The basic recording techniques for live sound events have not changed to accommodate this new dimension of sound field playback. More advanced analysis of sound fields and forensic capture of spatial sound also require new microphone array systems. This chapter describes a new spherical microphone array that performs an orthonormal decomposition of the sound pressure field. Sufficient order decomposition into these eigenbeams can produce much higher spatial resolution than traditional recording systems, thereby enabling more accurate sound field capture. A general mathematical framework based on these eigenbeams forms the basis of a scalable representation that enables one to easily compute and analyze the spatial distribution of live or recorded sound fields. A 24 element spherical microphone array composed of pressure microphones mounted on the surface of a rigid spherical baffle was constructed. Experimental results from a real-time implementation show that a theory based on spherical harmonic eigenbeams matches measured results.

Spherical Microphone Arrays for 3D Sound Recording

The progression of audio from monophonic to the present day 5‐channel playback is being driven by the desire to improve the immersion of the listener into the acoustic scene. In the limit, the goal is the reconstruction of the original sound field. This talk describes the decomposition of the sound field into orthogonal components, the so‐called spherical harmonics and is directly related to the method of Ambisonics. These components contain all required information to allow a reconstruction of the original sound field. This approach is scalable to any number of loudspeakers and is also backwards compatible to surround sound, stereo and mono playback. One problem is the recording of the orthogonal components. So far only solutions exist that allow the recording of spherical harmonics up to first order. This limits the spatial resolution. This presentation introduces a new microphone that overcomes this limitation. It consists of pressure sensors that are equally distributed on the surface of a rigid sphere. The number of sensors depends on the highest order spherical harmonic to be recorded. A minimum of (n+1)2 sensors is required to record harmonics up to nth order. The sensor signals are then processed to give the desired spherical harmonic outputs.

Jens Meyer

Papers

A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield

Noise-reducing directional microphone array

Audio system based on at least second-order eigenbeams

Spherical Microphone Arrays for 3D Sound Recording

A spherical microphone array for spatial sound recording