This thesis focuses on the phenomenon of aliasing and its mitigation with two explicit filters, i.e., Shuman and Padé filters. The Shuman filter is applied to velocity components of the Navier--Stokes equations. A derivation of this filter is presented as an approximation of a 1-D “pure math” mollifier and extend this to 2D and 3D. Analysis of the truncation error and wavenumber response is conducted with a range of grid spacings, Reynolds numbers and the filter parameter, β. Plots of the relationship between optimal filter parameter β and grid spacing, L2-norm error and Reynolds number to suggest ways to predict β are also presented. In order to guarantee that the optimal β is obtained under various stationary flow conditions, the power spectral density analysis of velocity components to unequivocally identify steady, periodic and quasi-periodic behaviours in a range of Reynolds numbers between 100 and 2000 are constructed. Parameters in Pade filters need not be changed. The two filters are applied to velocities in this paper on perturbed sine waves and a lid-driven cavity. Comparison is based on execution time, error and experimental results.