  We consider a recently proposed approach to graph signal processing based on
graphons. We show how the graphon-based approach to GSP applies to graphs
sampled from a stochastic block model. We obtain a basis for the graphon
Fourier transform on such samples directly from the link probability matrix and
the block sizes of the model. This formulation allows us to bound the
sensitivity of the Fourier transform to small changes in block sizes. We then
focus on the case where the probability matrix corresponds to a (weighted)
Cayley graph. If block sizes are equal, a nice Fourier basis can be derived
from the underlying group. We explore how, in the case where block sizes are
not equal, some or all nice properties of the group basis can be maintained. We
complement the theoretical results with simulations.
