A down-sampling operation is performed on moving image data to reduce a sample count of the data to 1/M times the original sample count. In the down-sampling operation, a band-limitation operation is performed on the moving image data using a low-pass filter. The low-pass filter has a stop band frequency that prevents a harmonic component having a K-th order or higher, of harmonic components generated in the down-sampling operation, from overlapping an original signal component. The down-sampling operation is then performed on the band-limited moving image data, thereby compressing the moving image data. Aliasing distortion caused by a harmonic component of a high order is controlled. The resulting compressed image is free from a substantial loss of a high-frequency component of the original signal.