IEEE Signal Processing Letters, vol. 4, no. 10, pp. 295-297, Oct. 1997

Loss of Perfect Reconstruction in Multidimensional Filterbanks and Wavelets Designed via Extended McClellan Transformations

Dong Wei, Brian L. Evans, and Alan C. Bovik

Department of Electrical and Computer Engineering, Engineering Science Building, The University of Texas at Austin, Austin, TX 78712-1084 USA

bevans@ece.utexas.edu - bovik@ece.utexas.edu

Abstract

Two extensions of the McClellan transformation have been proposed to transform even-length symmetric one-dimensional 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 FIR perfect reconstruction (PR) filter banks 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 filter banks are possible.

Last Updated 11/07/04.