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

• Published in: 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC) pp. 1141 - 1147
• Main Authors: Tay, David B. H., Ortega, Antonio, Anis, Aamir
• Format: Conference Proceeding
• Language: English
• Published: APSIPA organization 01-11-2018
• Subjects: Bipartite graph; Germanium; Graph Filter Banks; Matrices; Polyphase Structures; Spectral analysis; Spectral Graph Wavelets; Symmetric matrices; Transforms
• ISSN: 2640-0103
• DOI: 10.23919/APSIPA.2018.8659561

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.