Windowed fractional Fourier transform on graphs: Properties and fast algorithm

Fang Jia Yan; Bing Zhao Li

doi:10.1016/j.dsp.2021.103210

Windowed fractional Fourier transform on graphs: Properties and fast algorithm

Fang Jia Yan, Bing Zhao Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

A key challenge in the field of graph signal processing is to design proper transform methods to extract valuable information from signals on weighted graphs. This paper first defines convolution, translation and modulation operators in graph fractional domain, and proposes windowed graph fractional Fourier transform (WGFRFT). Related properties are proved. Then, a fast algorithm of WGFRFT is designed to increase flexibility. The robustness and superiority of the fast algorithm are verified via simulations with synthetic signals on graphs. Finally, an application to graph clustering is presented to show the practicability of WGFRFT.

Original language	English
Article number	103210
Journal	Digital Signal Processing: A Review Journal
Volume	118
DOIs	https://doi.org/10.1016/j.dsp.2021.103210
Publication status	Published - Nov 2021

Keywords

Fast algorithm
Fractional Fourier transform
Graph signal processing
Windowed graph Fourier transform

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Yan, F. J., & Li, B. Z. (2021). Windowed fractional Fourier transform on graphs: Properties and fast algorithm. Digital Signal Processing: A Review Journal, 118, Article 103210. https://doi.org/10.1016/j.dsp.2021.103210

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abstract = "A key challenge in the field of graph signal processing is to design proper transform methods to extract valuable information from signals on weighted graphs. This paper first defines convolution, translation and modulation operators in graph fractional domain, and proposes windowed graph fractional Fourier transform (WGFRFT). Related properties are proved. Then, a fast algorithm of WGFRFT is designed to increase flexibility. The robustness and superiority of the fast algorithm are verified via simulations with synthetic signals on graphs. Finally, an application to graph clustering is presented to show the practicability of WGFRFT.",

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AB - A key challenge in the field of graph signal processing is to design proper transform methods to extract valuable information from signals on weighted graphs. This paper first defines convolution, translation and modulation operators in graph fractional domain, and proposes windowed graph fractional Fourier transform (WGFRFT). Related properties are proved. Then, a fast algorithm of WGFRFT is designed to increase flexibility. The robustness and superiority of the fast algorithm are verified via simulations with synthetic signals on graphs. Finally, an application to graph clustering is presented to show the practicability of WGFRFT.

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Windowed fractional Fourier transform on graphs: Properties and fast algorithm

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Keywords

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