“…The proposed APS approach directly provides a mathematical formulation of the exact set of element excitations, which yield the desired APS without any iterative optimization process. Since the core calculations in the proposed approach rely on the FFT operations [ 29 , 30 , 31 , 32 , 33 , 34 ], the proposed method is computationally more efficient than the traditional optimization process, essentially coming down to trial and error [ 35 , 36 , 37 , 38 , 39 ]. Generally, it is assumed that the elements of linear array are uniformly spaced at distance d .…”