On the choice of rational decimation systems for multidimensional signals

Rational decimation systems, which alter the signal sampling rates by a rational factor, can be used to reduce the data rate of bandlimited signals without loss of information. In the present work, this idea is extended from the one-dimensional case to the multidimensional (MD) case. Given an arbitrary support of bandlimited MD signals, it is shown how to find a rational matrix whose irreducible left matrix fraction description defines the decimation and expansion matrices required in the rational decimation system. It is also shown how to choose the filter in this system to completely eliminate image components and aliasing effects. This technique is also applied to MD signals that are bandlimited in hyperspherical supports.<>