Parametric Time-Frequency Domain Spatial Audio

2 Spatial Decomposition by Spherical Array Processing

David Lou Alon and Boaz Rafaely

Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Israel

2.1 Introduction

Spherical microphone arrays have the advantageous property of rotational symmetry and are, therefore, most suitable for capturing and analyzing three-dimensional sound fields. A fundamental step in the spatial processing of microphone signals is to extract the plane waves that compose the measured sound field in an operation referred to as plane-wave decomposition (PWD; Meyer and Elko, 2002; Abhayapala and Ward, 2002; Gover et al., 2002; Rafaely, 2004). PWD provides a generic spatial representation of sound fields and was previously shown to be useful for various applications, such as beamforming (Meyer and Elko, 2002; Gover et al., 2002), sound field analysis (Abhayapala and Ward, 2002; Park and Rafaely, 2005), and spatial sound field recording (Gerzon, 1973; Abhayapala and Ward, 2002; Bertet et al., 2006; Jin et al., 2014). Chapter 3 of this book presents a PWD formulation that assumes spatial sparsity of the incident sound waves, is signal dependent, and under certain conditions achieves super-resolution with respect to the array capabilities.

An ideal PWD process that accurately estimates the plane-wave density around the microphone array typically requires high spatial resolution over a wide operating bandwidth. For spherical arrays, PWD is usually performed in the spherical ...