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Title: Lifted linear phase filter banks and the polyphase-with-advance representation

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 x{sub 0} with a filtered version of x{sub 1} and the second step updates x{sub 1} with a filtered version of x{sub 0}; 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 viamore » 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.« less
Authors:
 [1] ;  [2]
  1. (Christopher M.)
  2. (Brendt E.)
Publication Date:
OSTI Identifier:
977525
Report Number(s):
LA-UR-04-2088
TRN: US201009%%819
Resource Type:
Conference
Resource Relation:
Conference: Submitted to: 2004 IEEE Digital Signal Processing Workshop, August 2004, Taos, NM
Research Org:
Los Alamos National Laboratory
Sponsoring Org:
DOE
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGEBRA; FACTORIZATION; MATRICES; PROCESSING; SYNTHESIS