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Über dieses Buch

Recently, we proposed a completely novel and efficient way to design differential beamforming algorithms for linear microphone arrays. Thanks to this very flexible approach, any order of differential arrays can be designed. Moreover, they can be made robust against white noise amplification, which is the main inconvenience in these types of arrays. The other well-known problem with linear arrays is that electronic steering is not really feasible.

In this book, we extend all these fundamental ideas to circular microphone arrays and show that we can design small and compact differential arrays of any order that can be electronically steered in many different directions and offer a good degree of control of the white noise amplification problem, high directional gain, and frequency-independent response. We also present a number of practical examples, demonstrating that differential beamforming with circular microphone arrays is likely one of the best candidates for applications involving speech enhancement (i.e., noise reduction and dereverberation). Nearly all of the material presented is new and will be of great interest to engineers, students, and researchers working with microphone arrays and their applications in all types of telecommunications, security and surveillance contexts.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

In general, a microphone array refers to a sound acquisition system that uses multiple microphones to sample the sound field with spatial diversity. These microphones are arranged into a particular geometry in which each sensor’s position relative to a reference point is known to the subsequent processors.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 2. Problem Formulation

In this chapter, we explain some important aspects of beamforming and differential arrays with a focus on the circular geometry. The problem of a DMA design is formulated while we progress in defining some useful concepts. We start with the definition of the steering vector for a plane wave with the conventional anechoic farfield model, which has an interesting structure.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 3. Design of First-Order Circular Differential Arrays

This chapter is dedicated to the design of first-order circular differential microphone arrays with three sensors. We explore the dipole, cardioid, subcardioid, hypercardioid, and supercardioid.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 4. Design of Second-Order Circular Differential Arrays

This chapter is dedicated to the design of second-order circular differential microphone arrays with four and five sensors. The most well-known directivity patterns [1, 2] are designed and studied in each case.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 5. Design of Third-Order Circular Differential Arrays

In this chapter, we explore the design of third-order circular differential microphone arrays with six and seven sensors. In particular, we study a CDMA whose pattern has three distinct nulls [1]. We also generalize the approach to any CDMA order.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 6. Superdirective Beamforming with Circular Arrays

In this chapter, we derive all kind of superdirective beam formers for both linear and circular arrays. We also show how these beamformers are strongly related to DMAs as both approaches lead to large array gains, i.e., supergains.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 7. Minimum-Norm Solution for Robust Circular Differential Arrays

In this chapter, we show how the classical adaptive beamforming technique is related to differential circular arrays. From this important and useful relationship, we then derive a minimum-norm filter for the design of any order differential array, which can be robust against white noise amplification. This approach exploits the fact that the number of microphones can be much larger than the order of the CDMA. As a result, the more microphones, the more robust is the CDMA for a predetermined order.

Jacob Benesty, Jingdong Chen, Israel Cohen

Chapter 8. Design of Circular Differential Arrays with the Jacobi-Anger Expansion

In this chapter, we show that the patterns of differential arrays can be obtained from the general definition of the beampattern by approximating the exponential function with the Jacobi-Anger expansion. In other words, a directivity pattern of order N can be obtained from the Jacobi-Anger expansion of order N, as long as this approximation holds. We also explain how to design circular differential arrays based on this approach and their relationship to adaptive beamforming. Finally, we discuss the ideal beampattern and demonstrate that it can be designed like a CDMA.

Jacob Benesty, Jingdong Chen, Israel Cohen

Backmatter

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