On the McClellan transformation of 1-D even-length linear phase filterbanks

It was shown by Wei et al. (1997) that by applying the extended McClellan transformation on one-dimensional (1-D) even length linear phase perfect reconstruction (PR) filterbanks (FBs), the resulting multidimensional (M-D) FB does not have the PR property. The two types of extended McClellan transformation that were considered in Wei et al. were originally proposed by Mersereau et al. (1976) and Karam (1996), respectively, for the design of single filters. We shall show in this letter that by using a different type of transformation, PR can indeed be preserved in the M-D FB. A new class of transformation that achieves PR is presented. Furthermore, by choosing an appropriate transformation the M-D filters will have linear phase.