Study and Design of Differential Microphone Arrays by Jacob Benesty, Jingdong Chen

By Jacob Benesty, Jingdong Chen

Microphone arrays have attracted loads of curiosity during the last few many years seeing that they've got the aptitude to resolve many vital difficulties reminiscent of noise reduction/speech enhancement, resource separation, dereverberation, spatial sound recording, and resource localization/tracking, to call a number of. even if, the layout and implementation of microphone arrays with beamforming algorithms isn't a trivial activity in terms of processing broadband indications akin to speech. certainly, in so much sensor preparations, the beamformer output has a tendency to have a frequency-dependent reaction. One exception, possibly, is the relatives of differential microphone arrays (DMAs) who've the promise to shape frequency-independent responses. furthermore, they've got the capability to achieve excessive directional earnings with small and compact apertures. consequently, this sort of microphone arrays has drawn a lot examine and improvement awareness lately. This e-book is meant to supply a scientific learn of DMAs from a sign processing viewpoint. the first aim is to improve a rigorous yet but easy theory

for the layout, implementation, and function research of DMAs. the speculation contains a few sign processing ideas for the layout of standard first-order, second-order, third-order, and in addition the final Nth-order DMAs. for every order, specific examples are given on the best way to shape usual directional styles akin to the dipole, cardioid, supercardioid, hypercardioid, subcardioid, and quadrupole. The examine demonstrates the functionality of the various order DMAs when it comes to beampattern, directivity issue, white noise achieve, and achieve for element resources. The inherent courting among differential processing and adaptive beamforming is mentioned, which supplies a greater knowing of DMAs and why they could in attaining excessive directional achieve. eventually, we express tips on how to layout DMAs that may be powerful opposed to white noise amplification.

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45) Interestingly, the farther away is the null from the main lobe, the smaller is the range of frequencies that can be affected by white noise amplification. This fact intuitively makes sense since by putting the null closer to the main lobe, the two constraints that shape the directional pattern will be conflicting more with each other. 34) will be ill conditioned. As a result, the uncorrelated white noise at the two microphones will be amplified. The best possible situation (where the two constraints are the farthest away and, hence, the linear system is best conditioned) is a null at θ = 180◦ , which corresponds to the cardioid.

5. H. Cox, R. M. Zeskind, and M. M. Owen, “Robust adaptive beamforming,” IEEE Trans. , vol. ASSP-35, pp. 1365–1376, Oct. 1987. 6. G. W. -T. Nguyen Pong, “A steerable and variable first-order differential microphone array,” in Proc. IEEE ICASSP, 1997, pp. 223–226. 7. R. M. M. Derkx and K. Janse, “Theoretical analysis of a first-order azimuth-steerable superdirective microphone array,” IEEE Trans. , vol. 17, pp. 150–162, Jan. 2011. Chapter 4 Study and Design of Second-Order Differential Arrays In this chapter, we study and design the most important second-order differential microphone arrays.

In this case, we have exactly two constraints to fulfill. The first constraint is the distortionless response (a one at the angle θ = 0◦ ) and the second constraint is a null in the interval 0◦ < θ ≤ 180◦ . 2) where α1,1 = cos θ1,1 is given by design (a null at the angle θ1,1 ) with −1 ≤ α1,1 < 1. 2) as dH (ω, 1) 1 h (ω) = . 3) is recognized to be a 2 × 2 Vandermonde matrix. 3) and the obtained solution is the best we can get from a mathematical point of view. J. Benesty and J. 1007/978-3-642-33753-6_3, © Springer-Verlag Berlin Heidelberg 2013 33 33 3 Study and Design of First-Order Differential Arrays 34 34 3 First-Order Differential Arrays θ 2 1 δ − + 1 ω Fig.

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