Multi-dimensional sampling rate conversion

The multi-dimensional sampling theorem is explained. A mathematical description is used that makes possible the computation of the spectrum for regular and irregular (but periodic) sampling lattices. The N-dimensional conversion between two signals sampled with arbitrary sampling lattices is then presented in the frequency domain. The required ideal filters are given. After that the conversion is described as an N-dimensional time variant system. A structure for the realization is presented. An application of B=2 is the television standards conversion.