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Vertex-Frequency Energy Distributions

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Book cover Vertex-Frequency Analysis of Graph Signals

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

Vertex-varying spectral content on graphs challenge the assumption of vertex invariance, and require vertex-frequency representations to adequately analyze them. The localization window in graph Fourier transform plays a crucial role in this analysis. An analysis of the window functions is presented. The corresponding spectrograms are considered from the energy condition point of view as well. Like in time-frequency analysis, the distribution of signal energy as a function of the vertex and spectral indices is an alternative way to approach vertex-frequency analysis. After an introduction to the second part of this chapter, a local smoothness definition, a definition of an ideal form of the vertex-frequency energy distributions, and two energy forms of the vertex-frequency representations are given. A graph form of the Rihaczek distribution is used as the basic distribution to define a class of reduced interference vertex-frequency energy distributions. These distributions reduce cross-terms effects and satisfy graph signal marginal properties. The theory is illustrated through examples.

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Acknowledgements

Ervin Sejdić acknowledges the support of the NSF CAREER grant number 1652203.

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Authors and Affiliations

  1. University of Montenegro, Podgorica, Montenegro

    Ljubiša Stanković & Miloš Daković

  2. University of Pittsburg, Pittsburg, PA, USA

    Ervin Sejdić

Authors
  1. Ljubiša Stanković
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  2. Miloš Daković
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  3. Ervin Sejdić
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Correspondence to Ljubiša Stanković .

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Editors and Affiliations

  1. Faculty of Electrical Engineering, University of Montenegro, Podgorica, Montenegro

    Ljubiša Stanković

  2. Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Ervin Sejdić

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Stanković, L., Daković, M., Sejdić, E. (2019). Vertex-Frequency Energy Distributions. In: Stanković, L., Sejdić, E. (eds) Vertex-Frequency Analysis of Graph Signals. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-03574-7_11

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  • DOI: https://doi.org/10.1007/978-3-030-03574-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03573-0

  • Online ISBN: 978-3-030-03574-7

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