Extending Spectral Factorization to the Near-Field Synthesis of Shaped Beams

We introduce a new approach to the mask-constrained power-pattern synthesis of 1-D shaped beams lying in arbitrary masks on a line of the near-field zone. The proposed technique leverages and unifies the well-known spectral factorization method and warping sampling strategies able to restore the bandlimitedness of the near field. By so doing, it is possible to cast the overall synthesis as a linear programming problem followed by a polynomial factorization. The approach also allows apriori identifying the minimum source size required to fulfill a given power-pattern mask.