Sampling is a necessity in minifying a digital image. In the event that the image contains spatial frequencies higher than half the sampling frequencies in any dimensions, aliasing will occur. Aliasing in minifying digital images with and without prefiltering are compared. Using the Shannon sampling theorem, the reduction of aliasing is explained based on the Fourier transform, instead of the discrete wavelet transform. It is found that one should not consider only the classical quality evaluation measures of the sampled image when selecting from the several antialiasing methods, we should also consider the particular requirements of some key local information, such as to make letters or Chinese characters more recognizable, although the degree of aliasing reduction may be lowered.