Group Lifting Structures For Multirate Filter Banks, I: Uniqueness Of Lifting Factorizations
- Los Alamos National Laboratory
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.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 957812
- Report Number(s):
- LA-UR-08-04755; LA-UR-08-4755; TRN: US201016%%208
- Journal Information:
- IEEE Transactions on Signal Processing, Journal Name: IEEE Transactions on Signal Processing
- Country of Publication:
- United States
- Language:
- English
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