  Hilbert space fusion frames are a natural extension of Hilbert space frames,
extending the notion from a set of vectors in a Hilbert space to a set of
subspaces of a Hilbert space with analogous notions of overcompleteness and
boundedness. As tight frames are a very important topic within standard frame
theory, tight fusion frames are similarly important; however, only trivial
examples of tight fusion frames are hitherto known. In this paper, we apply
ideas from Gabor analysis to demonstrate a non-trivial construction of tight
fusion frames. We then use this construction to further show their
applicability in some cases for the retrieval of signals modulo phase.
