Abstract
The signal processing on graphs has been widely used in various fields, including machine learning, classification and network signal processing, in which the sampling of bandlimited graph signals plays an important role. In this paper, we discuss the sampling of bandlimited graph signals based on the theory of function spaces, which is consistent with the pattern of the Shannon sampling theorem. First, we derive an interpolation operator by constructing bandlimited space of graph signals, and the corresponding sampling operator is also obtained. Based on the relationship between the interpolation and sampling operators, a sampling theorem for bandlimited graph signals is proposed, and its physical meaning in the graph frequency domain is also given. Furthermore, the implementation of the proposed theorem via matrix calculation is discussed.
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Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants 61501144 and 61671179, in part by the Fundamental Research Funds for the Central Universities under Grant 01111305, and in part by the National Basic Research Program of China under Grant 2013CB329003.
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© 2018 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
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Han, M., Shi, J., Deng, Y., Song, W. (2018). On Sampling of Bandlimited Graph Signals. In: Gu, X., Liu, G., Li, B. (eds) Machine Learning and Intelligent Communications. MLICOM 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 227. Springer, Cham. https://doi.org/10.1007/978-3-319-73447-7_62
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DOI: https://doi.org/10.1007/978-3-319-73447-7_62
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