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On Hilbert transform, analytic signal, and modulation analysis for signals over graphs
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0003-2638-6047
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.ORCID iD: 0000-0002-2718-0262
2019 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 156, p. 106-115Article in journal (Refereed) Published
Abstract [en]

We propose Hilbert transform and analytic signal construction for signals over graphs. This is motivated by the popularity of Hilbert transform, analytic signal, and modulation analysis in conventional signal processing, and the observation that complementary insight is often obtained by viewing conventional signals in the graph setting. Our definitions of Hilbert transform and analytic signal use a conjugate symmetry-like property exhibited by the graph Fourier transform (GFT), resulting in a 'one-sided' spectrum for the graph analytic signal. The resulting graph Hilbert transform is shown to possess many interesting mathematical properties and also exhibit the ability to highlight anomalies/discontinuities in the graph signal and the nodes across which signal discontinuities occur. Using the graph analytic signal, we further define amplitude, phase, and frequency modulations for a graph signal. We illustrate the proposed concepts by showing applications to synthesized and real-world signals. For example, we show that the graph Hilbert transform can indicate presence of anomalies and that graph analytic signal, and associated amplitude and frequency modulations reveal complementary information in speech signals.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 156, p. 106-115
Keywords [en]
Graph signal processing, Analytic signal, Hilbert transform, Demodulation, Anomaly detection
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-240988DOI: 10.1016/j.sigpro.2018.10.016ISI: 000453494200011Scopus ID: 2-s2.0-85056192636OAI: oai:DiVA.org:kth-240988DiVA, id: diva2:1277490
Note

QC 20190110

Available from: 2019-01-10 Created: 2019-01-10 Last updated: 2019-06-11Bibliographically approved

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Venkitaraman, ArunChatterjee, SaikatHändel, Peter

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  • apa
  • harvard1
  • ieee
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  • vancouver
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
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  • nn-NB
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Output format
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