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The Fast Fourier Transform (FFT) can be applied to circular arrays receiving wideband sonar radiation. As with conventional beamforming, the FFT serves in the first stage to divide the spectrum into narrow frequency bands. Then the array element responses of each band are analyzed in a second stage of FFTs for the Fourier components (modes) of the array excitation function for the respective band. Application of weights of the mode responses, to simulate the radiation efficiency of the modes for any given element radiation pattern and to control the array pattern, yields the Fourier components of the beam pattern. To integrate these Fourier components, inverse FFTs follow which yield as many beam pattern samples as there are array elements.
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