Fundamentals of Spherical Array Processing

This book provides a comprehensive introduction to the theory and practice of sphericalmicrophone arrays, and was written for graduate students, researchers and engineers whowork with spherical microphone arrays in a wide range of applications. The new editionincludes additions and modifications, and references supplementary Matlab codeto provide the reader with a straightforward start for own implementations. The book is alsoaccompanied by a Matlab manual, which explains how to implement the examples andsimulations presented in the book. The first two chapters provide the reader with the necessary mathematical and physicalbackground, including an introduction to the spherical Fourier transform and the formulationof plane-wave sound fields in the spherical harmonic domain. In turn, the third chapter coversthe theory of spatial sampling, employed when selecting the positions of microphones tosample sound pressure functions in space. Subsequent chapters highlight various spherical array configurations, including the popularrigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonicsdomain, including axis-symmetric beamforming, and the performance measures of directivityindex and white noise gain are introduced, and a range of optimal beamformers for sphericalarrays, including those that achieve maximum directivity and maximum robustness aredeveloped, along with the Dolph-Chebyshev beamformer. The final chapter discusses moreadvanced beamformers, such as MVDR (minimum variance distortionless response) andLCMV (linearly constrained minimum variance) types, which are tailored to the measuredsound field. Mathworks kindly distributes the Matlab sources for this book on https://www.mathworks.com/matlabcentral/fileexchange/68655-fundamentals-of-spherical-array-processing.