Vaidyanathan, P. P. and Chen, Tsuhan (1995) Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals. IEEE Transactions on Signal Processing, 43 (5). pp. 1090-1102. ISSN 1053-587X http://resolver.caltech.edu/CaltechAUTHORS:VAIieeetsp95b
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In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed.
|Additional Information:||© Copyright 1995 IEEE. Reprinted with permission. Manuscript received October 29, 1993; revised November 1, 1994. This work was supported by Office of Naval Research under Grant N00014-93-1-0231, Tektronix, Inc., and Rockwell, International. The associate editor coordinating the review of this paper and approving it for publication was Dr. Truong Nguyen. Some of the results in Sections IV and V were proved by the first author in response to interesting questions raised by Prof. R.J. McEliece (Caltech) in the context of convolutional coding theory and questions raised by Dr. A. Soman (past Caltech student).|
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