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In the context of signal processing, array synthesis involves the creation of an array of antennas to achieve a specific radiation pattern, while beamforming is a technique used to direct the radiation pattern of the antenna array in a specific direction. Both of these techniques are widely used in fields such as telecommunications, radar, sonar, and acoustics, among others. It is important to note that the successful implementation of these techniques requires a deep understanding of the underlying principles and careful consideration of factors such as the number and placement of antennas, the frequency of the signal, and the desired radiation pattern.