Frame-Theoretic Analysis of Oversampled Filter Banks - Signal Processing, IEEE Transactions on
نویسندگان
چکیده
We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (IIR) uniform filter banks (FB’s). Our analysis is based on a new relationship between the FB’s polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FB’s providing perfect reconstruction. We find necessary and sufficient conditions for an oversampled FB to provide a frame expansion. A new frame-theoretic procedure for the design of paraunitary FB’s from given nonparaunitary FB’s is formulated. We show that the frame bounds of an FB can be obtained by an eigenanalysis of the polyphase matrices. The relevance of the frame bounds as a characterization of important numerical properties of an FB is assessed by means of a stochastic sensitivity analysis. We consider special cases in which the calculation of the frame bounds and synthesis filters is simplified. Finally, simulation results are presented.
منابع مشابه
Oversampled Filter Banks - Signal Processing, IEEE Transactions on
Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in `(Z). These frames are the subject of this paper. First, necessary and sufficient conditions on a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Comp...
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