Teke, Oguzhan and Vaidyanathan, P. P.
(2018)
*Energy Compaction Filters on Graphs.*
In:
2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP).
IEEE
, Piscataway, NJ, pp. 783-787.
ISBN 978-1-7281-1295-4.
http://resolver.caltech.edu/CaltechAUTHORS:20190228-154232324

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## Abstract

In classical signal processing spectral concentration is an important problem that was first formulated and analyzed by Slepian. The solution to this problem gives the optimal FIR filter that can confine the largest amount of energy in a specific bandwidth for a given filter order. The solution is also known as the prolate sequence. This study investigates the same problem for polynomial graph filters. The problem is formulated in both graph-free and graph-dependent fashions. The graph-free formulation assumes a continuous graph spectrum, in which case it becomes the polynomial concentration problem. This formulation has a universal approach that provides a theoretical reference point. However, in reality graphs have discrete spectrum. The graph-dependent formulation assumes that the eigenvalues of the graph are known and formulates the energy compaction problem accordingly. When the eigenvalues of the graph have a uniform distribution, the graph-dependent formulation is shown to be asymptotically equivalent to the graph-free formulation. However, in reality eigenvalues of a graph tend to have different densities across the spectrum. Thus, the optimal filter depends on the underlying graph operator, and a filter cannot be universally optimal for every graph.

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Additional Information: | © 2018 IEEE. This work was supported in parts by the ONR grants N00014-18-1-2390 and N00014-17-1-2732, the NSF grant CCF-1712633, and the Electrical Engineering Carver Mead Research Seed Fund of the California Institute of Technology. | ||||||||||

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Subject Keywords: | Graph signal processing, polynomial filters, concentrated polynomials, Hilbert matrix | ||||||||||

Record Number: | CaltechAUTHORS:20190228-154232324 | ||||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20190228-154232324 | ||||||||||

Official Citation: | O. Teke and P. P. Vaidyanathan, "ENERGY COMPACTION FILTERS ON GRAPHS," 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Anaheim, CA, USA, 2018, pp. 783-787. doi: 10.1109/GlobalSIP.2018.8646570 | ||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||

ID Code: | 93366 | ||||||||||

Collection: | CaltechAUTHORS | ||||||||||

Deposited By: | Tony Diaz | ||||||||||

Deposited On: | 28 Feb 2019 23:49 | ||||||||||

Last Modified: | 28 Feb 2019 23:49 |

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