Oversampled FIR and IIR DFT filter banks and Weyl-Heisenberg frames

We apply the theory of Weyl-Heisenberg frames (WHFs) to oversampled FIR and IIR DFT filter banks (FBs). We show that the polyphase matrices provide a matrix representation of the frame operator and we find conditions on a DFT FB to provide a WHF expansion. We also show that paraunitary and biorthogonal DFT FBs correspond to tight and exact WHFs, respectively, and that the same bounds can be obtained by an eigenanalysis of the polyphase matrices. Simulation results demonstrate the importance of the frame bounds for the design of DFT FBs.