  The operator that first truncates to a neighborhood of the origin in the
spectral domain then truncates to a neighborhood of the origin in the spatial
domain is investigated in the case of Boolean cubes. This operator is self
adjoint on a space of bandlimited signals. The eigenspaces of this iterated
projection operator are studied and are shown to depend fundamentally on the
neighborhood structure of the cube when regarded as a metric graph with path
distance equal to Hamming distance.
