Frame-theoretic analysis and design of oversampled filter banks

Authors

Helmut Bölcskei, Franz Hlawatsch, and Hans G. Feichtinger

Reference

Proc. of IEEE International Symposium on Circuits and Systems (ISCAS), Atlanta (GA), Vol. 2, pp. 409-412, May 1996.

DOI: 10.1109/ISCAS.1996.541733

Abstract

We provide a frame-theoretical analysis of oversampled and critically sampled, FIR and IIR, uniform filter banks (FBs). Our analysis is based on a relation between the polyphase matrices and the frame operator. For a given oversampled analysis FB, we parameterize all synthesis FBs providing perfect reconstruction, and we discuss the minimum norm synthesis FB and its approximative construction. We find necessary and sufficient conditions for a FB to provide a frame expansion. It is shown that paraunitary FBs correspond to tight frames and biorthogonal FBs correspond to exact frames. A new procedure for the design of paraunitary FBs is formulated. We show that the frame bounds can be obtained by an eigenanalysis of the polyphase matrices, and that they determine important numerical properties of the FB.

Keywords

Oversampled filter banks, FIR, IIR, frame theory, design freedom, noise reduction

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