Extending DSP to Graph Signal Processing: The Companion Approach.

Graph signal processing (GSP) was designed in [1] (see also [2], [3]), as a natural, intuitive extension of traditional discrete signal processing (DSP). Concepts such as shifting, filtering, graph signal, graph Fourier transform, and graph spectral analysis are naturally extended from DSP to GSP. However, other concepts, such as delta functions, sampling, and graph structure cannot be naturally extended. This illustrates a gap between DSP and GSP when introducing new concepts to GSP: DSP intuitions do not necessarily hold for GSP and GSP cannot naturally draw inspiration from DSP. The GSP companion model developed in [4] solves this issue by bridging the gap between GSP and DSP in the literature. In this paper, we show several examples of graphs, their signals, and their corresponding companion models, following the work in [4]. We illustrate some properties of the GSP companion model discussed in [4] using these examples.