Actions for Lifted linear phase filter banks and the polyphase-with-advance representation [electronic resource].

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Lifted linear phase filter banks and the polyphase-with-advance representation [electronic resource].

Published
Washington, D.C. : United States. Dept. of Energy, 2004.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy
Physical Description
2 pages : digital, PDF file
Additional Creators
Los Alamos National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary
A matrix theory is developed for the noncausal polyphase-with-advance representation that underlies the theory of lifted perfect reconstruction filter banks and wavelet transforms as developed by Sweldens and Daubechies. This theory provides the fundamental lifting methodology employed in the ISO/IEC JPEG-2000 still image coding standard, which the authors helped to develop. Lifting structures for polyphase-with-advance filter banks are depicted in Figure 1. In the analysis bank of Figure 1(a), the first lifting step updates x0 with a filtered version of x1 and the second step updates x1 with a filtered version of x0; gain factors 1/K and K normalize the lowpass- and highpass-filtered output subbands. Each of these steps is inverted by the corresponding operations in the synthesis bank shown in Figure 1(b). Lifting steps correspond to upper- or lower-triangular matrices, S{sub i}(z), in a cascade-form decomposition of the polyphase analysis matrix, H{sub a}(z). Lifting structures can also be implemented reversibly (i.e., losslessly in fixed-precision arithmetic) by rounding the lifting updates to integer values. Our treatment of the polyphase-with-advance representation develops an extensive matrix algebra framework that goes far beyond the results of. Specifically, we focus on analyzing and implementing linear phase two-channel filter banks via linear phase lifting cascade schemes. Whole-sample symmetric (WS) and half-sample symmetric (HS) linear phase filter banks are characterized completely in terms of the polyphase-with-advance representation. The theory benefits significantly from a number of new group-theoretic structures arising in the polyphase-with-advance matrix algebra from the lifting factorization of linear phase filter banks.
Report Numbers
E 1.99:la-ur-04-2088
la-ur-04-2088
Subject(s)
Note
Published through SciTech Connect.
01/01/2004.
"la-ur-04-2088"
Submitted to: 2004 IEEE Digital Signal Processing Workshop, August 2004, Taos, NM.
Brislawn, C. M. (Christopher M.); Wohlberg, B. E. (Brendt E.).
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