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A new class of two-channel biorthogonal filter banks and wavelet bases

Phoong, See-May and Kim, Chai W. and Vaidyanathan, P. P. and Ansari, Rashid (1995) A new class of two-channel biorthogonal filter banks and wavelet bases. IEEE Transactions on Signal Processing, 43 (3). pp. 649-665. ISSN 1053-587X. http://resolver.caltech.edu/CaltechAUTHORS:PHOieeetsp95a

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Abstract

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters.


Item Type:Article
Additional Information:© Copyright 1995 IEEE. Reprinted with permission. Manuscript received October 8, 1993; revised August 18, 1994. This work was supported by Office of Naval Research under Grant N00014-93-0231 and funds from Tektronix, Inc. The associate editor coordinating the review of this paper and approving it for publication was Prof. Roberto H. Bamberger. The authors would like to thank Dr. T. Chen of AT&T Bell Labs, and I. Djokovic, graduate student of California Institute of Technology, Pasadena, for fruitful discussions. Dr. Chen also provided the software for the allpass design using the eigenfilter approach for Example 3.1.
Subject Keywords:FIR filters, IIR filters, computational complexity, delay circuits, signal reconstruction, signal synthesis, stability, transfer functions, two-dimensional digital filters, wavelet transforms, zero assignment
Record Number:CaltechAUTHORS:PHOieeetsp95a
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:PHOieeetsp95a
Alternative URL:http://dx.doi.org/10.1109/78.370620
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8709
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:07 Sep 2007
Last Modified:26 Dec 2012 09:41

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