Understanding the Basis of Graph Signal Processing via an Intuitive Example-Driven Approach [Lecture Notes]

Graphs are irregular structures that naturally represent the multifaceted data attributes; however, traditional approaches have been established outside signal processing and largely focus on analyzing the underlying graphs rather than signals on graphs. Given the rapidly increasing availability of multisensor and multinode measurements, likely recorded on irregular or ad hoc grids, it would be extremely advantageous to analyze such structured data as "signals on graphs" and thus benefit from the ability of graphs to incorporate spatial sensing awareness, physical intuition, and sensor importance, together with the inherent "local versus global" sensor association. The aim of this lecture note is, therefore, to establish a common language between graph signals that are observed in irregular signal domains and some of the most fundamental paradigms in digital signal processing (DSP), such as spectral analysis, system transfer function, digital filter design, parameter estimation, and optimal denoising.