  We prove that the most common filtering procedure for nodal discontinuous
Galerkin (DG) methods is stable. The proof exploits that the DG approximation
is constructed from polynomial basis functions and that integrals are
approximated with high-order accurate Legendre-Gauss-Lobatto quadrature. The
theoretical discussion serves to re-contextualize stable filtering results for
finite difference methods into the DG setting. It is shown that the stability
of the filtering is equivalent to a particular contractivity condition borrowed
from the analysis of so-called transmission problems. As such, the temporal
stability proof relies on the fact that the underlying spatial discretization
of the problem possesses a semi-discrete bound on the solution. Numerical tests
are provided to verify and validate the underlying theoretical results.
