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Extending Classical Multirate Signal Processing Theory to Graphs - Part II: M-Channel Filter Banks

Teke, Oguzhan and Vaidyanathan, P. P. (2017) Extending Classical Multirate Signal Processing Theory to Graphs - Part II: M-Channel Filter Banks. IEEE Transactions on Signal Processing, 65 (2). pp. 423-437. ISSN 1053-587X. https://resolver.caltech.edu/CaltechAUTHORS:20161025-123628985

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Abstract

This paper builds upon the basic theory of multirate systems for graph signals developed in the companion paper (Part I) and studiesM-channel polynomial filter banks on graphs. The behavior of such graph filter banks differs from that of classical filter banks in many ways, the precise details depending on the eigenstructure of the adjacency matrix A. It is shown that graph filter banks represent (linear and) periodically shift-variant systems only when A satisfies the noble identity conditions developed in Part I. It is then shown that perfect reconstruction graph filter banks can always be developed when A satisfies the eigenvector structure satisfied by M-block cyclic graphs and has distinct eigenvalues (further restrictions on eigenvalues being unnecessary for this). If A is actually M-block cyclic then these PR filter banks indeed become practical, i.e., arbitrary filter polynomial orders are possible, and there are robustness advantages. In this case the PR condition is identical to PR in classical filter banks – any classical PR example can be converted to a graph PR filter bank on an M-block cyclic graph. It is shown that for M-block cyclic graphs with all eigenvalues on the unit circle, the frequency responses of filters have meaningful correspondence with classical filter banks. Polyphase representations are then developed for graph filter banks and utilized to develop alternate conditions for alias cancellation and perfect reconstruction, again for graphs with specific eigenstructures. It is then shown that the eigenvector condition on the graph can be relaxed by using similarity transforms.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TSP.2016.2620111DOIArticle
http://ieeexplore.ieee.org/document/7605459/PublisherArticle
ORCID:
AuthorORCID
Teke, Oguzhan0000-0002-1131-5206
Additional Information:© 2016 IEEE. Manuscript received July 28, 2015; revised February 12, 2016 and July 29, 2016; accepted October 4, 2016. Date of publication October 21, 2016; date of current version November 17, 2016. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Pierre Borgnat. This work was supported in part by the Office of Naval Research under Grant N00014-11-1-0676 and Grant N00014-15-1-2118, and in part by the California Institute of Technology.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1-0676
Office of Naval Research (ONR)N00014-15-1-2118
CaltechUNSPECIFIED
Subject Keywords:Multirate processing, graph signals, filter banks on graphs, aliasing on graphs, block-cyclic graphs
Issue or Number:2
Record Number:CaltechAUTHORS:20161025-123628985
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161025-123628985
Official Citation:O. Teke and P. P. Vaidyanathan, "Extending Classical Multirate Signal Processing Theory to Graphs—Part II: M-Channel Filter Banks," in IEEE Transactions on Signal Processing, vol. 65, no. 2, pp. 423-437, Jan.15, 15 2017. doi: 10.1109/TSP.2016.2620111 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7605459&isnumber=7748608
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71456
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Oct 2016 20:12
Last Modified:03 Oct 2019 16:07

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