A window function is a mathematical function that is zero valued outside some chosen interval [1] , [2] . For applications like filtering, detection, and estimation, the window functions take the form of limited time functions, which are in general real and even functions [3] , [4] , while for applications like beamforming and image processing, they are limited spatial functions. A spatial window can be a complex function for optimizing the beams in magnitude as well as in phase, as in the case of certain antenna arrays, where the phasor currents in the array are complex numbers [5].