Multidimensional causal, stable, perfect reconstruction filter banks

Following our recent work on the design and parametrization of one-dimensional, causal, stable, perfect reconstruction subband coding schemes, we show that very similar results hold in multi-dimensions as well. Such considerations are far more non-trivial, however, due to difficulties characteristic of the algebra of multi-variable polynomials and rational functions. As in 1-D, both frequency as well as state space domain descriptions of complete parametrization and design methods turn out to be feasible in the multidimensional case. While the need for causal, stable schemes in nonseparable subband coding is substantiated, at the same time we raise and discuss the issue of genericity of the PR property in multidimensional problems. Examples are included to partially illustrate the central theme of the work reported