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A new windowed digraph Fourier transform

Le, Trung Thanh and Nguyen, Linh Trung and Nguyen, Viet Dung and Abed-Meraim, Karim (2019) A new windowed digraph Fourier transform. Technical Report. University of Engineering and Technology, Vietnam National University, Hanoi, Vietnam.

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Signal processing on graphs is an emerging topic of signal processing, considering graphs as signals. Hence, similar concepts and tools in signal processing can be extended, for understanding graph signals, such as graph frequency, graph operators, graph Fourier transform. In this report, we focus on the joint relationship of vertex-frequency representation of graphs. Motivated by the existing relationship between the incidence matrix and the Laplacian matrix for undirected graphs, we define a generalized Laplacian matrix for directed graphs. This allows us to propose a unified framework for the graph Fourier transform, graph modulation and graph translation. Then, built upon the graph modulation and translation operators, we propose a new windowed graph Fourier transform which a tight vertex-frequency frame. The experimental results indicate that our proposed methods are better than state-of-the-art methods and beneficial for analyzing various different types of graphs, including directed, undirected, weighted, unweighted and connected graphs.

Item Type: Technical Report (Technical Report)
Additional Information: UET-AVITECH-2019001
Subjects: Electronics and Communications
Information Technology (IT)
Divisions: Advanced Insitute of Engineering and Technology (AVITECH)
Depositing User: A/Prof. Linh Trung Nguyen
Date Deposited: 23 Apr 2019 20:09
Last Modified: 24 Apr 2019 12:44

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