LOSS OF PERFECT RECONSTRUCTION IN MULTIDIMENSIONAL FILTERBANKS AND WAVELETS DESIGNED VIA EXTENDED MCCLELLAN TRANSFORMATIONS

Two extensions of the McClellan transformation have been proposed to t ransform even-length symmetric one-dimensional (1-D) prototype filters into even/odd-length multidimensional filters. We show that, unlike t he original McClellan transformation, the two extended McClellan trans formations 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 ally t ransformation function that can preserve PR after transformation, Howe ver, for one of the transformations, we point out that near-PR filterb anks are possible.