"I am looking for some simple concrete examples of the ways in which real problems go through graph signal processing and how graph Fourier transforms are obtained."
• A concrete example of a graph Fourier transform, to the Minnesota road network, is presented in Fourier Analysis on Graphs; another example, to genetic profiling for cancer subtype classification, is discussed in Graph SP: Fundamentals and Applications.
• To obtain the graph Fourier transform you could use the Matlab routine GSP_GFT in the Graph Signal Processing Toolbox.