Frame-theoretic analysis of oversampled filter banks

We provide a frame-theoretic analysis of oversampled finite impulse respons e (FIR) and infinite impulse response (FIR) uniform filter banks (FB's), Ou r analysis is based on a new relationship between the FB's polyphase matric es and the frame operator corresponding to an FB. For a given oversampled a nalysis FB, we present a parameterization of all synthesis FB's providing p erfect reconstruction. We find necessary and sufficient conditions for an o versampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FB's from given nonparaunitary FB's is formu lated. We show that the frame bounds of an FB can be obtained by an eigen-a nalysis of the polyphase matrices. The relevance of the frame bounds as a c haracterization of important numerical properties of an FB is assessed by m eans of a stochastic sensitivity analysis. We consider special cases in whi ch the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented.