Rotation of a two-dimensional sampling set using one-dimensional resampling

Generating intermediate sample points from a two-dimensional sample set generally requires two-dimensional filtering. Because true two-dimensional filtering requires a large number of computations, alternative filtering methods may be attractive. One alternative is to perform a series of one-dimensional filtering operations on individual lines of samples within the two-dimensional set. As long as the Nyquist sampling rate in both dimensions is satisfied at each intermediate step, valid sample values result. This paper analyzes a one-dimensional interpolation procedure for resampling a two-dimensional set of samples taken on an orthogonal grid into a second set of samples on an orthogonal grid which is rotated with respect to the first. The mathematical analysis quantifies the minimum sampling rate requirements, for a function with a rectangular band limit, as a function of the two-dimensional bandwidths and the angle of rotation between the two sampling grids.