A fast method for calculating the radiation patterns of unequally spaced vibrators

A fast Fourier transform method is proposed for calculating the radiation patterns of unequally spaced vibrators. The method makes it possible to calculate the directivity factor approximately but with sufficient accuracy; furthermore, a significant increase in computational time is achieved as compared with the indirect method. Results obtained with the FFT method are compared with those obtained with the direct method for a seven-element synphase equal-amplitude system of isotropic radiators.