Loss of perfect reconstruction in multidimensional filterbanks and wavelets designed via extended McClellan transformations

Two extensions of the McClellan transformation have been proposed to transform even-length symmetric one-dimensional (1-D) prototype filters into even/odd-length multidimensional filters. We show that, unlike the original McClellan transformation, the two extended McClellan transformations suffer from a limitation in the design of multidimensional two-channel finite impulse response (FIR) perfect reconstruction (PR) filterbanks and wavelets in the sense that there does not exist any transformation function that can preserve PR after transformation, However, for one of the transformations, we point out that near-PR filterbanks are possible.