Design of frequency-invariant beamformers employing multi-dimensional Fourier transforms

The design of a class of broadband arrays with frequency invariant beam patterns is studied and a simplified version of the design method employing multi-dimensional Fourier transforms is proposed with detailed account of each step. In the design examples, we give a mathematical explanation for the failure of this method in the lower frequencies. For a design with main beam pointing to a direction other than the broadside, the frequency invariant property is not good and two solutions for this problem are provided.