Efficient Continuous Beam Steering for Planar Arrays of Differential Microphones

Performing continuous beam steering, from planar arrays of high-order differential microphones, is not trivial. The main problem is that shape-preserving beams can be steered only in a finite set of privileged directions, which depend on the position and the number of physical microphones. In this letter, we propose a simple and computationally inexpensive method for alleviating this problem using planar microphone arrays. Given two identical reference beams pointing in two different directions, we show how to build a beam of nearly constant shape, which can be continuously steered between such two directions. The proposed method, unlike the diffused steering approaches based on linear combinations of eigenbeams (spherical harmonics), is applicable to planar arrays also if we deal with beams characterized by high-order polar patterns. Using the coefficients of the Fourier series of the polar patterns, we also show how to find a tradeoff between shape invariance of the steered beam, and maximum angular displacement between the two reference beams. We show the effectiveness of the proposed method through the analysis of models based on first-, second-, and third-order differential microphones

On the Design and Implementation of Higher Order Differential Microphones

A novel systematic approach to the design of directivity patterns of higher order differential microphones is proposed. The directivity patterns are obtained by optimizing a cost function which is a convex combination of a front-back energy ratio and uniformity within a frontal sector of interest. Most of the standard directivity patterns-omnidirectional, cardioid, subcardioid, hypercardioid, supercardioid-are particular solutions of this optimization problem with specific values of two free parameters: the angular width of the frontal sector and the convex combination factor. More general solutions of practical use are obtained by varying these two parameters. Many of these optimal directivity patterns are trigonometric polynomials with complex roots. A new differential array structure that enables the implementation of general higher order directivity patterns, with complex or real roots, is then proposed. The effectiveness of the proposed design framework and the implementation structure are illustrated by design examples, simulations, and measurements