A novel method is proposed for spectrally  shaping the beamforming weights quantization error at the  sub-array layer where the in-band distortion intends to  move into a position where the sub-array factor has high  attenuation. To do that, the sub-array factor or the  composite sub-array factor is tiled by the periodicity of the  ultimate-layer array factor. Then, the digital filter layout is  designed based on the superposition of all tiles intersecting  with the visible region of the overall array factor (O-AF),  and the O-AF is spectrally shaped to minimize the number  of bits quantifying the beamforming weights. The method is  investigated for analog, digital, and hybrid array  beamforming with multi-layer overlapped sub-array  systems of different sizes and shapes. Its performance is  promising and potent in alleviating the overall array factor  distortion in all cases.