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.