Estimation of the acoustic field directionality by use of planar and volumetric arrays via the Fourier series method and the Fourier integral method

The possibility of estimating the directionality of a stationary homogeneous noise field, directly from the element outputs of a line array, is investigated and found to be feasible for large arrays without encountering ill conditioning. This technique, called inverse beamforming for historical reasons, is applicable to line and planar as well as volumetric arrays, and requires no more than two‐dimensional fast Fourier transforms (FFTs) for its realization. Derivations and results are presented both for a Fourier series method and a Fourier integral method.