Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon Fourier transform and linear shift invariant graphon filters , the graphon counterparts of the graph Fourier transform and graph filters. It is shown that for convergent sequences of graphs and associated graph signals: (i) the graph Fourier transform converges to the graphon Fourier transform when the graphon signal is bandlimited; (ii) the spectral and vertex responses of graph filters converge to the spectral and vertex responses of graphon filters with the same coefficients. These theorems imply that for graphs that belong to certain families, i.e., that are part of sequences that converge to a certain graphon, graph Fourier analysis and graph filter design have well defined limits. In turn, these facts extend applicability of graph signal processing to graphs with large number of nodes — since signal processing pipelines designed for limit graphons can be applied to finite graphs — and to dynamic graphs — since we can relate the result of SP pipelines designed for different graphs from the same convergent graph sequence.

中文翻译：

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图形信号处理

Graphons 是无限维的对象，当它们的节点数趋于无穷大时，它代表了图的收敛序列的极限。本文推导了一个以图形信号处理为中心的理论图形傅里叶变换和线性位移不变性 graphon filters ，图傅立叶变换和图滤波器的graphon对应物。结果表明，对于收敛的图序列和相关的图信号： (i) 当图子信号是带限的时，图傅立叶变换收敛到图子傅立叶变换；(ii) 图形滤波器的频谱和顶点响应收敛到具有相同系数的图形滤波器的频谱和顶点响应。这些定理意味着，对于属于某些族的图，即收敛到某个图子的序列的一部分，图傅立叶分析和图滤波器设计具有明确定义的限制。反过来，