A modular antenna array consists of multiple subarrays (modules) with flexible inter-module spacing. Compared to conventional uniformly spaced arrays, modular architectures can achieve enhanced spatial resolution by exploiting a larger effective aperture through flexible deployment. However, wide inter-module spacing inherently generates strong interfering lobes that degrade beamforming performance in both the far-field and near-field. To overcome this, we propose tapered aperture sampling (TAS), a spatial design framework that arranges modules according to a continuous tapering window for a fixed antenna aperture. TAS systematically suppresses grating lobes while preserving the standard half-wavelength spacing within each module.