Graphon Signal Processing

Graphons are infinite-dimensional objects that represent the limit of convergent sequences graphs as their number nodes goes to infinity. This paper derives a theory graphon signal processing centered on notions Fourier transform and linear shift invariant filters, counterparts graph filters. It is shown for associated signals: (i) converges when bandlimited; (ii) spectral vertex responses filters converge with same coefficients. These theorems imply belong certain families, i.e., part graphon, analysis filter design have well defined limits. In turn, these facts extend applicability large -- since pipelines designed graphons can be applied finite dynamic we relate result SP different from sequence.