Fundamentals of Spherical Array Processing

  • Boaz Rafaely

Part of the Springer Topics in Signal Processing book series (STSP, volume 16)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Boaz Rafaely
    Pages 1-31
  3. Boaz Rafaely
    Pages 33-58
  4. Boaz Rafaely
    Pages 59-80
  5. Boaz Rafaely
    Pages 81-102
  6. Boaz Rafaely
    Pages 103-125
  7. Boaz Rafaely
    Pages 127-156
  8. Boaz Rafaely
    Pages 157-186
  9. Back Matter
    Pages 187-193

About this book


This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays, and was written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The new edition includes additions and modifications, and references supplementary Matlab code to provide the reader with a straightforward start for own implementations. The book is also accompanied by a Matlab manual, which explains how to implement the examples and simulations presented in the book.

The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. In turn, the third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space.

Subsequent chapters highlight various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, including those that achieve maximum directivity and maximum robustness are developed, along with the Dolph–Chebyshev beamformer. The final chapter discusses more advanced beamformers, such as MVDR (minimum variance distortionless response) and LCMV (linearly constrained minimum variance) types, which are tailored to the measured sound field.


Linearly Constrained Minimum Variance (LCMV) Microphone Arrays Minimum Variance Distortionless Response (MVDR) Optimal Beamforming Plane-Wave Decomposition Rigid Sphere Array Spatial Sampling Spherical Fourier Transform Spherical Harmonics Spherical Array Beamforming Spherical Array Configurations Spherical Arrays Spherical Microphone Arrays Matlab Spherical Algorithm

Authors and affiliations

  • Boaz Rafaely
    • 1
  1. 1.Department of Electrical and Computer EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-99560-1
  • Online ISBN 978-3-319-99561-8
  • Series Print ISSN 1866-2609
  • Series Online ISSN 1866-2617
  • Buy this book on publisher's site