The generation of periodic synthetic turbulence through superposition of Fourier modes is investigated. The introduction of directional biases and mismatches in the second-order statistics associated with the enforcement of periodicity is analyzed and quantified. Two strategies for mitigation of these disparities are proposed. The suggested approaches are subsequently validated and compared with the original methodologies using direct numerical simulations. The proposed strategies are capable of neutralizing the disparities in the second-order statistics at the injection region. The development from synthetic to realistic turbulence is evaluated through the resulting flow statistics and spectral analysis. It is found that higher-order statistics and other indicators converge to the expected results with sufficient length.