Graph Signal Processing in a Nutshell

The framework of graph signal processing was conceived in the last decade with the ambition of generalizing the tools from classical digital signal processing to the case in which the signal is defined over an irregular structure modelled by a graph. Instead of discrete time - what one would call a regular 1-D domain, in which a signal sample is adjacent to only two neighbors and for any pair of contiguous samples the distance is the same - the signals here are defined over graphs and, therefore, the distance and relations between adjacent samples vary along the signal. For instance, one may consider the temperature signal defined from the data of a sensor mesh network. When creating the tools in such a scenario, many challenges arise even with basic concepts of the classical theory. In this paper, the core ideas of graph signal processing are presented, focusing on the two main frameworks developed along the years, and a couple of examples and applications are shown. We conclude drawing attention to a few of the many open opportunities for further studies in the field.