  The emerging field of graph signal processing (GSP) allows to transpose
classical signal processing operations (e.g., filtering) to signals on graphs.
The GSP framework is generally built upon the graph Laplacian, which plays a
crucial role to study graph properties and measure graph signal smoothness.
Here instead, we propose the graph modularity matrix as the centerpiece of GSP,
in order to incorporate knowledge about graph community structure when
processing signals on the graph, but without the need for community detection.
We study this approach in several generic settings such as filtering, optimal
sampling and reconstruction, surrogate data generation, and denoising.
Feasibility is illustrated by a small-scale example and a transportation
network dataset, as well as one application in human neuroimaging where
community-aware GSP reveals relationships between behavior and brain features
that are not shown by Laplacian-based GSP. This work demonstrates how concepts
from network science can lead to new meaningful operations on graph signals.
