Signal processing on weighted line graphs

Aliaksei Sandryhaila, Jelena Kovacevic

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter describes a signal processing framework for signals that are represented, or indexed, by weighted line graphs, which are a generalization of directed line graphs used for representation of time signals in classical signal processing theory. The presented framework is based on the theory of discrete signal processing on graphs and on algebraic signal processing theory. It defines fundamental signal processing concepts, such as signals and filters, z-transform, frequency and spectrum, Fourier transform and others, in a principled way. The framework also illustrates a strong connection between signal processing on weighted line graphs and signal representation based on orthogonal polynomials.

Original languageEnglish (US)
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages245-259
Number of pages15
Edition9783319201870
DOIs
StatePublished - Jan 1 2015

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319201870
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Line Graph
Weighted Graph
Signal Processing
Signal processing
Directed line
z transform
Directed Graph
Orthogonal Polynomials
Fourier transform
Fourier transforms
Polynomials
Mathematical transformations
Filter
Graph in graph theory
Framework

Keywords

  • Algebraic signal processing
  • Graph filter
  • Graph fourier transform
  • Graph frequency
  • Orthogonal polynomials
  • Signal processing on graphs

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Sandryhaila, A., & Kovacevic, J. (2015). Signal processing on weighted line graphs. In Applied and Numerical Harmonic Analysis (9783319201870 ed., pp. 245-259). (Applied and Numerical Harmonic Analysis; No. 9783319201870). Springer International Publishing. https://doi.org/10.1007/978-3-319-20188-7_10

Signal processing on weighted line graphs. / Sandryhaila, Aliaksei; Kovacevic, Jelena.

Applied and Numerical Harmonic Analysis. 9783319201870. ed. Springer International Publishing, 2015. p. 245-259 (Applied and Numerical Harmonic Analysis; No. 9783319201870).

Research output: Chapter in Book/Report/Conference proceedingChapter

Sandryhaila, A & Kovacevic, J 2015, Signal processing on weighted line graphs. in Applied and Numerical Harmonic Analysis. 9783319201870 edn, Applied and Numerical Harmonic Analysis, no. 9783319201870, Springer International Publishing, pp. 245-259. https://doi.org/10.1007/978-3-319-20188-7_10
Sandryhaila A, Kovacevic J. Signal processing on weighted line graphs. In Applied and Numerical Harmonic Analysis. 9783319201870 ed. Springer International Publishing. 2015. p. 245-259. (Applied and Numerical Harmonic Analysis; 9783319201870). https://doi.org/10.1007/978-3-319-20188-7_10
Sandryhaila, Aliaksei ; Kovacevic, Jelena. / Signal processing on weighted line graphs. Applied and Numerical Harmonic Analysis. 9783319201870. ed. Springer International Publishing, 2015. pp. 245-259 (Applied and Numerical Harmonic Analysis; 9783319201870).
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