On the choice of rational decimation systems for multidimensional signals

Abstract

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 this paper, we extend this idea from the one-dimensional case to the multidimensional (MD) case. Given an arbitrary support of bandlimited MD signals, we show how to find a rational matrix whose irreducible left matrix fraction description defines the decimation and expansion matrices required in the rational decimation system. Furthermore, we show how to choose the filter in this system to completely eliminate image components and aliasing effects. We also apply this technique to MD signals that are bandlimited in hyperspherical supports.