Spectral Tetris Fusion Frame Constructions

Spectral tetris is a flexible and elementary method to derive unit norm frames with a given frame operator having all of its eigenvalues ≥ 2. One important application of this method is to construct fusion frames. We will give necessary and sufficient conditions for a spectral tetris construction to give a fusion frame with prescribed eigenvalues for its fusion frame operator and with prescribed dimensions for its subspaces. This answers one of the major open problems in this area. We then generalize spectral tetris to use building blocks of size larger than 2 × 2 to construct unit norm tight frames of redundancy smaller then 2 and use it to derive non-equidimensional tight fusion frames having all eigenvalues of the fusion frame operator equal to λ ∈ [1, 2).