Frame-theoretic analysis of oversampled filter banks

  • Authors:

  • H. Bolcskei;F. Hlawatsch;H.G. Feichtinger

  • Affiliations:

  • Inst. fur Nachrichtentech., Vienna Univ. of Technol.;-;-

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 1998

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Abstract

We provide a frame-theoretic analysis of oversampled finite impulse response (FIR) and infinite impulse response (FIR) uniform filter banks (FBs). Our analysis is based on a new relationship between the FBs polyphase matrices and the frame operator corresponding to an FB. For a given oversampled analysis FB, we present a parameterization of all synthesis FBs 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 FBs from given nonparaunitary FBs is formulated. We show that the frame bounds of an FB can be obtained by an eigen-analysis 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