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Communication

Random-Walk Laplacian for Frequency Analysis in Periodic Graphs

SPCOM Group, Universitat Politècnica de Catalunya-Barcelona Tech, 08034 Barcelona, Spain
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Academic Editor: Adam Idzkowski
Sensors 2021, 21(4), 1275; https://doi.org/10.3390/s21041275
Received: 20 December 2020 / Revised: 6 February 2021 / Accepted: 7 February 2021 / Published: 11 February 2021
(This article belongs to the Section Sensor Networks)
This paper presents the benefits of using the random-walk normalized Laplacian matrix as a graph-shift operator and defines the frequencies of a graph by the eigenvalues of this matrix. A criterion to order these frequencies is proposed based on the Euclidean distance between a graph signal and its shifted version with the transition matrix as shift operator. Further, the frequencies of a periodic graph built through the repeated concatenation of a basic graph are studied. We show that when a graph is replicated, the graph frequency domain is interpolated by an upsampling factor equal to the number of replicas of the basic graph, similarly to the effect of zero-padding in digital signal processing. View Full-Text
Keywords: graph Fourier transform; frequency ordering; random-walk Laplacian; periodic graph graph Fourier transform; frequency ordering; random-walk Laplacian; periodic graph
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MDPI and ACS Style

Boukrab, R.; Pagès-Zamora, A. Random-Walk Laplacian for Frequency Analysis in Periodic Graphs. Sensors 2021, 21, 1275. https://doi.org/10.3390/s21041275

AMA Style

Boukrab R, Pagès-Zamora A. Random-Walk Laplacian for Frequency Analysis in Periodic Graphs. Sensors. 2021; 21(4):1275. https://doi.org/10.3390/s21041275

Chicago/Turabian Style

Boukrab, Rachid, and Alba Pagès-Zamora. 2021. "Random-Walk Laplacian for Frequency Analysis in Periodic Graphs" Sensors 21, no. 4: 1275. https://doi.org/10.3390/s21041275

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