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Title: Group Lifting Structures For Multirate Filter Banks, I: Uniqueness Of Lifting Factorizations

This paper studies two-channel finite impulse response (FIR) perfect reconstruction filter banks. The connection between filter banks and wavelet transforms is well-known and will not be treated here. Figure 1 depicts the polyphase-with-advance representation of a filter bank [6]. A lifting factorization, is a factorization of polyphase matrices into upper and lower triangular lifting matrices. The existence of such decompositions via the Euclidean algorithm was shown for general FIR perfect reconstruction filter banks in [9] and was subsequently refined for linear phase filter banks in [10], [6]. These latter works were motivated by the ISO JPEG 2000 image coding standard [11], [12], [10], which specifies whole-sample symmetric (WS, or FIR type 1 linear phase) filter banks, as in Figure 2(a), in terms of half-sample symmetric (RS, or FIR type 2) lifting filters.
Authors:
 [1]
  1. Los Alamos National Laboratory
Publication Date:
OSTI Identifier:
957812
Report Number(s):
LA-UR-08-04755; LA-UR-08-4755
TRN: US201016%%208
DOE Contract Number:
AC52-06NA25396
Resource Type:
Journal Article
Resource Relation:
Journal Name: IEEE Transactions on Signal Processing
Research Org:
Los Alamos National Laboratory (LANL)
Sponsoring Org:
DOE
Country of Publication:
United States
Language:
English
Subject:
42; ALGORITHMS; FACTORIZATION; FIRS; MATRICES