Fundamentals of Spherical Array Processing

  • Boaz Rafaely

Part of the Springer Topics in Signal Processing book series (STSP, volume 8)

Table of contents

  1. Front Matter
    Pages i-x
  2. Boaz Rafaely
    Pages 1-30
  3. Boaz Rafaely
    Pages 31-55
  4. Boaz Rafaely
    Pages 57-77
  5. Boaz Rafaely
    Pages 79-99
  6. Boaz Rafaely
    Pages 101-123
  7. Boaz Rafaely
    Pages 125-153
  8. Boaz Rafaely
    Pages 155-182
  9. Back Matter
    Pages 183-193

About this book


This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. 

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.

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 present 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 beamformers that achieve maximum directivity and maximum robustness, and the Dolph-Chebyshev beamformer are developed. The final chapter discusses more advanced beamformers, such as MVDR and LCMV, 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

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-Verlag Berlin Heidelberg 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-662-45663-7
  • Online ISBN 978-3-662-45664-4
  • Series Print ISSN 1866-2609
  • Series Online ISSN 1866-2617
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