We consider a recently proposed approach to graph signal processing based on graphons. We show how the graphon-based approach to GSP applies to graphs sampled from a stochastic block model. We obtain a basis for the graphon Fourier transform on such samples directly from the link probability matrix and the block sizes of the model. This formulation allows us to bound the sensitivity of the Fourier transform to small changes in block sizes. We then focus on the case where the probability matrix corresponds to a (weighted) Cayley graph. If block sizes are equal, a nice Fourier basis can be derived from the underlying group. We explore how, in the case where block sizes are not equal, some or all nice properties of the group basis can be maintained. We complement the theoretical results with simulations.

翻译：我们考虑一种最近提出的基于图元的图信号处理方法。我们展示了这种基于图元的GSP方法如何应用于从随机块模型采样的图。我们直接从模型的链接概率矩阵和块大小中，为此类样本上的图元傅里叶变换获得了一个基。该公式使我们能够界定傅里叶变换对块大小微小变化的敏感性。随后，我们聚焦于概率矩阵对应于一个（加权）凯莱图的情况。如果块大小相等，则可以从底层群导出一个良好的傅里叶基。我们探讨了在块大小不相等的情况下，如何保持群基的部分或全部良好性质。我们通过仿真对理论结果进行了补充。