Terry L. Henderson
Terry J. Brudner
Appl. Research Labs., The Univ. of Texas, Austin, TX 78713-8029
The use of a pressure gradient microphone for detecting the source direction of an incident plane wave is well known. Furthermore, any receiving aperture that applies a specified apodization can be regarded as extracting a point-sample of a spatially filtered version of the incident wave. Our result is that when the gradient method is applied to the spatially filtered wave (which is also a plane wave), the answer can be expressed in terms modified apodizations, formed from the originally specified apodization function and its vector gradient, integrated over the original aperture and/or its boundary, together with simple temporal filters. Fortunately, this seemingly complicated structure collapses to a much simpler one in many cases of interest, and it is even possible to extend the method to the higher order case in which two or more wave directions are detected simultaneously. Alternatively, one wave direction can be measured while steering a broadband null in another specified direction, and the steered-null direction can be altered dynamically even after beamforming. Examples are given. Our results are especially applicable to transient sounds of arbitrary bandwidth. [Work supported by ARL:UT IR&D.]