Pan Chao, Benesty Jacob, Chen Jingdong
Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi'an, Shaanxi 710072, China.
INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, Suite 6900, Montreal, Quebec H5A 1K6, Canada.
J Acoust Soc Am. 2015 Aug;138(2):1079-89. doi: 10.1121/1.4927690.
Differential microphone arrays have the potential to be widely deployed in hands-free communication systems thanks to their frequency-invariant beampatterns, high directivity factors, and small apertures. Traditionally, they are designed and implemented in a multistage way with uniform linear geometries. This paper presents an approach to the design of differential microphone arrays with orthogonal polynomials, more specifically with Jacobi polynomials. It first shows how to express the beampatterns as a function of orthogonal polynomials. Then several differential beamformers are derived and their performance depends on the parameters of the Jacobi polynomials. Simulations show the great flexibility of the proposed method in terms of designing any order differential microphone arrays with different beampatterns and controlling white noise gain.
差分麦克风阵列因其频率不变的波束图、高指向性因子和小孔径而有潜力在免提通信系统中广泛部署。传统上，它们是以具有均匀线性几何结构的多阶段方式设计和实现的。本文提出了一种用正交多项式，更具体地说是用雅可比多项式来设计差分麦克风阵列的方法。它首先展示了如何将波束图表示为正交多项式的函数。然后推导了几种差分波束形成器，其性能取决于雅可比多项式的参数。仿真结果表明，该方法在设计具有不同波束图的任意阶差分麦克风阵列以及控制白噪声增益方面具有很大的灵活性。
