  Multivariate signals, which are measured simultaneously over time and
acquired by sensor networks, are becoming increasingly common. The emerging
field of graph signal processing (GSP) promises to analyse spectral
characteristics of these multivariate signals, while at the same time taking
the spatial structure between the time signals into account. A central idea in
GSP is the graph Fourier transform, which projects a multivariate signal onto
frequency-ordered graph Fourier modes, and can therefore be regarded as a
spatial analog of the temporal Fourier transform. This chapter derives and
discusses key concepts in GSP, with a specific focus on how the various
concepts relate to one another. The experimental section focuses on the role of
graph frequency in data classification, with applications to neuroimaging. To
address the limited sample size of neurophysiological datasets, we introduce a
minimalist simulation framework that can generate arbitrary amounts of data.
Using this artificial data, we find that lower graph frequency signals are less
suitable for classifying neurophysiological data as compared to higher graph
frequency signals. Finally, we introduce a baseline testing framework for GSP.
Employing this framework, our results suggest that GSP applications may
attenuate spectral characteristics in the signals, highlighting current
limitations of GSP for neuroimaging.
