  The application of graph signal processing (GSP) on partially observed graph
signals with missing nodes has gained attention recently. This is because
processing data from large graphs are difficult, if not impossible due to the
lack of availability of full observations. Many prior works have been developed
using the assumption that the generated graph signals are smooth or low pass
filtered. This paper treats a blind graph filter detection problem under this
context. We propose a detector that certifies whether the partially observed
graph signals are low pass filtered, without requiring the graph topology
knowledge. As an example application, our detector leads to a pre-screening
method to filter out non low pass signals and thus robustify the prior GSP
algorithms. We also bound the sample complexity of our detector in terms of the
class of filters, number of observed nodes, etc. Numerical experiments verify
the efficacy of our method.
