Multidimensional perfect reconstruction filter banks with generalized subsampling

It is shown how a class of nonlattice sampling grids can be analyzed, and required PR (perfect reconstruction) conditions for the two-band subband decomposition are derived. This is done through the generalization of the sampling operation involved in the multirate systems. By generalizing sub/up-sampling operations, new degrees of freedom are introduced which can be used to facilitate the filter design problem. It can be shown that for a specific analysis filter bank, PR might be possible with one sampling strategy and not with the other ones. Therefore, the design of filter banks should be considered as a joint sampling/filter design problem.<>