On Sampling of Bandlimited Graph Signals

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.