Uncertainty Principle on Graphs

Graph Signal Processing (GSP) is a mathematical framework that aims at extending classical Fourier harmonic analysis to irregular domains described using graphs. Within this framework, authors have proposed to define operators (e.g. translations, convolutions) and processes (e.g. filtering, sampling). A very important and fundamental result in classical harmonic analysis is the uncertainty principle, which states that a signal cannot be localized both in time and in frequency domains. In this chapter, we explore the uncertainty principle in the context of GSP. More precisely, we present notions of graph and spectral spreads, and show that the existence of signals that are both localized in the graph domain and in the spectrum domain depends on the graph.

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