System theoretic ideas for construction of ND in (N⩾2) causal, stable, perfect reconstruction filter banks

We show that it is possible to have a large family of perfect reconstruction multidimensional (n-D) subband coding filter banks, which are causal, stable and IIR both at the analysis and at the synthesis ends. Complete parameterization of such classes of filters leading to design methods are given. Parameterizations in frequency domain terms as well as in terms of state space descriptions of filters are provided. The development is valid for two-band as well as for multi-band subband coding schemes. Our development is also valid for dilation matrices other than the conventional quincunx subsampling. Thus, sampling density ratios other than two are implicit in the development resulting from the fact that we consider multi-band subband coding schemes for arbitrary decimation and interpolation matrices