  This paper proposes a blind detection problem for low pass graph signals.
Without assuming knowledge of the exact graph topology, we aim to detect if a
set of graph signal observations are generated from a low pass graph filter.
Our problem is motivated by the widely adopted assumption of low pass
(a.k.a.~smooth) signals required by many existing works in graph signal
processing (GSP), as well as the longstanding problem of network dynamics
identification. Focusing on detecting low pass graph signals on modular graphs
whose cutoff frequency coincides with the number of clusters in the graph, we
propose to leverage the unique spectral pattern exhibited by such low pass
graph signals. We analyze the sample complexity of these detectors considering
the effects of graph filter's properties, random delays, and other parameters.
We show novel applications of the blind detector on robustifying graph
learning, identifying antagonistic ties in opinion dynamics, and detecting
anomalies in power systems. Numerical experiments validate our findings.
