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This paper describes a class of multibeam synthesis algorithms that are useful for large arrays when simultaneous ing of interference is required. In these algorithms, the computational cost is kept small by using fast Fourier transform (FFT) beamforming, while at the same time interference is ed using spatial projections. Once the interference steering vectors are determined, these algorithms have a computational cost per output which is only slightly greater than that of the FFT with no interference ing. In addition, techniques are derived that allow the Fourier beams to be protected against distortion by constraining the patterns, reducing the pattern variation, or both. These techniques may be particularly well suited for some new radiotelescopes now in the planning stages.