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Time domain and frequency domain concepts which aid in the design and efficient implementation of a digital beamformer have been described at various times in the literature. The numerous beam-former structures that result are discussed with an emphasis on hardware requirements and spectral areas of application. Time domain procedures which include delay-sum, partial-sum, interpolation and shifted-sideband beamforming, and frequency domain techniques which include the application of discrete Fourier transforms and phase shift beam-forming are considered. Hardware considerations are primarily in the areas of analog-to-digital conversion, data storage, and computational throughput requirements.