Steerable Circular Differential Microphone Arrays

An efficient continuous beam steering method, applicable to differential microphones of any order, has been recently developed. Given two identical reference beams, pointing in two different directions, the method allows to derive a beam of nearly constant shape continuously steerable between those two directions. In this paper, the steering method is applied to robust Differential Microphone Arrays (DMAs) characterized by uniform circular array geometries. In particular, a generalized filter performing the steering operation is defined. The definition of such a filter enables the derivation of closed-form formulas for computing the white noise gain and the directivity factor of the designed steerable differential beamformers for any frequency of interest. A study on the shape invariance of the steered beams is conducted. Applications of the steering approach to first-, second-and third-order robust circular DMAs are presented.