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Fundamentals of Differential Beamforming

Part of the SpringerBriefs in Electrical and Computer Engineering Book Series

DOI: 10.1007/978-981-10-1046-0

ISBN: 978-981-10-1045-3

Publisher: Springer Singapore - Springer Journals

Apr 28, 2016

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Introduction

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 1 –12

[In this chapter, we briefly discuss microphone array beamforming in general and differential beamforming in particular. We also explain why this latter approach is fundamental and should be considered in most speech and audio acquisition systems.]
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Problem Formulation

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 13 –26

[In this chapter, we describe the signal model, formulate the problem, and explain how differential beamforming works. We discuss the most fundamental performance measures such as the beampattern, the front-to-back ratio, the signal-to-noise ratio gain, the white noise gain, and the directivity...
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Some Background

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 27 –39

[In this chapter, we present in a very concise way some fundamental aspects of linear spaces, orthogonal functions, and orthogonal polynomials. Three family of orthogonal polynomials (Legendre, Chebyshev, and Jacobi), of great importance to us, are discussed. Most of the presented results are...
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Performance Measures Revisited

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 41 –50

[In this chapter, we revisit some of the most fundamental performance measures associated with differential beamforming.]
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Conventional Optimization

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 51 –79

[With conventional optimization techniques, we can derive a large class of differential beamformers as it is shown in this chapter. From some classical quadratic criteria, we introduce the w-hypercardioid and the w-supercardioid of any order. We also propose robust versions of them. We reveal how...
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Beampattern Design

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 81 –110

[Beampattern designBeampattern design is an important topic in array signal processing in general. This chapter is dedicated to this matter but in the particular context of differential beamforming. From the different definitions and approximations of the beampatterns, we show how to design any...
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Joint Optimization

Benesty, Jacob; Chen, Jingdong; Pan, Chao

Pages: 111 –120

[When designing a differential beamformer, it is of great importance to consider the white noise amplification problem and the array frequency response. Combining some results from the two previous chapters and exploiting the array redundancy, we show in the following how to derive differential...

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