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

It was recently shown by Wei ct al, [1] that by applying the extended McCle llan transformation on one-dimensional (1-D) even-length linear phase perfe ct reconstruction (PR) filterbanks (PB's), the resulting multidimensional ( M-D) PB does not have the PR property, The two types of extended McClellan transformation that was considered in [1] were originally proposed by Merse reau ct al, [2] and Karam [3], respectively, for the design of single filte rs. We shall show in this letter that by using a different type of transfor mation, PR can indeed be preserved in the M-D FB, A new class of transforma tion that achieves PR will be presented, Furthermore, by choosing an approp riate transformation the M-D filters will have linear phase.