This piece of work replicates on the antenna array thinning exploring the benefits of known Fourier Analysis. In this communication Fourier transform is applied to the synthesis of periodic arrays for minimizing the Peak Side Lobe (PSL) level and thereby enhancing the directivity. Furthermore, the concept of Fill Factor (degree of thinning), i.e., reduction in the number of active elements is experimented for the above said objective. The proposed methodology is worked out on periodic linear and planar arrays. Numerical study and simulation results are composed with array thinning designs from literature. The analysis demonstrates the superiority of the illustrated Fourier technique.