Near-Field Synthesis of 1-D Shaped Patterns through Spectral Factorization and Minimally-Redundant Array-Like Representations

We introduce a novel approach for the mask-constrained power synthesis of 1-D fields enabling near-field shaping according to arbitrary masks. This method presents an innovative framework based on the spectral factorization technique and a warping strategy, allowing for an accurate representation of the near field as a minimally redundant bandlimited function. This provides valuable theoretical tools to effectively solve the problem. In fact, the synthesis is formulated as a linear programming problem followed by a polynomial factorization. Additionally, the approach allows for the a-priori identification of the minimum size of the source required to fulfill a given near-field intensity mask.