Frame-theoretic analysis of oversampled filter banks

Author

Bolcskei, Helmut ; Hlawatsch, Franz ; Feichtinger, Hans G.

Author_Institution

Inst. fur Nachrichtentech., Vienna Univ. of Technol., Austria

Volume

46

Issue

12

fYear

1998

fDate

12/1/1998 12:00:00 AM

Firstpage

3256

Lastpage

3268

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

Keywords

FIR filters; IIR filters; channel bank filters; eigenvalues and eigenfunctions; mathematical operators; matrix algebra; signal reconstruction; signal sampling; stochastic processes; FIR uniform filter banks; eigen-analysis; frame bounds; frame expansion; frame operator; frame-theoretic analysis; infinite impulse response; necessary conditions; oversampled filter banks; perfect reconstruction; polyphase matrices; simulation results; stochastic sensitivity analysis; sufficient conditions; synthesis filters; Channel bank filters; Computational efficiency; Filter bank; Finite impulse response filter; IIR filters; Mathematics; Sensitivity analysis; Signal synthesis; Stochastic processes; Sufficient conditions;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.735301

Filename

735301