Filter Banks on Discrete Abelian Groups

Abstract

In this work we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multidimensional or cyclic filter banks as well as filter banks for signals in ${\ell }^2({\mathbb{Z}}^d\times {\mathbb{Z}}_s)$ or ${\ell }^2({\mathbb{Z}}_r\times {\mathbb{Z}}_s)$ spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds.

This version is the same as the previous one except some comments on the polyphase transform and some references have been added