This paper presents a new approach to extract the physical poles of antennas. The Singularity Expansion Method (SEM) allows modelling the antenna backscattering using poles which are theoretically independent of the wave incident angle, making them useful for antenna identification. Nevertheless, only the physical poles respect this property while the spurious poles change for each incident angle. Indeed, we call physical the poles linked to the antenna itself and spurious the poles linked to anything but the antenna (excitation, noise…). The goal of this paper is to highlight the method to define the optimal time windowing applied on the antenna backscattering in order to obtain the physical poles of the antenna. The approach is based on the Window Decreasing Technique and the Window Increasing Technique. The SEM is applied on the backscattered field measured in the boresight direction of three antennas: a narrowband patch antenna, a wideband helix antenna and a UWB antenna. By using these poles to reconstruct the field backscattered in several directions, we show that the poles extracted from one direction with this new approach are relevant to reconstruct the backscattered field for any other directions. Moreover, we show that these poles can be extracted directly from these other directions.