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Role of anticausal inverses in multirate filter-banks. II. The FIR case, factorizations, and biorthogonal lapped transforms

Vaidyanathan, P. P. and Chen, Tsuhan (1995) Role of anticausal inverses in multirate filter-banks. II. The FIR case, factorizations, and biorthogonal lapped transforms. IEEE Transactions on Signal Processing, 43 (5). pp. 1103-1115. ISSN 1053-587X. doi:10.1109/78.382396.

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For pt. I see ibid., vol.43, no.5, p.1090, 1990. In part I we studied the system-theoretic properties of discrete time transfer matrices in the context of inversion, and classified them according to the types of inverses they had. In particular, we outlined the role of causal FIR matrices with anticausal FIR inverses (abbreviated cafacafi) in the characterization of FIR perfect reconstruction (PR) filter banks. Essentially all FIR PR filter banks can be characterized by causal FIR polyphase matrices having anticausal FIR inverses. In this paper, we introduce the most general degree-one cafacafi building block, and consider the problem of factorizing cafacafi systems into these building blocks. Factorizability conditions are developed. A special class of cafacafi systems called the biorthogonal lapped transform (BOLT) is developed, and shown to be factorizable. This is a generalization of the well-known lapped orthogonal transform (LOT). Examples of unfactorizable cafacafi systems are also demonstrated. Finally it is shown that any causal FIR matrix with FIR inverse can be written as a product of a factorizable cafacafi system and a unimodular matrix.

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1995 IEEE. Reprinted with permission. Manuscript received October 29, 1993; revised November 1, 1994. This work was supported by the 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.
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