Cascade and Lifting Structures in the Spectral Domain for Bipartite Graph Filter Banks

In classical multirate filter bank systems, the cascade (product) of simple polyphase matrices is an important technique for the theory, design and implementation of filter banks. A particularly important class of cascades uses elementary matrices and leads to the well known lifting scheme in wavelets. In this paper the theory and principles of cascade and lifting structures for bipartite graph filter banks are developed. Accurate spectral characterizations of these structures using equivalent subgraphs will be presented. Some features of the structures in the graph case, that are not present in the classical case, will be discussed.