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Chris Brislawn and Brendt Wohlberg, "Gain Normalization of Lifted Filter Banks", Signal Processing, vol. 87, no. 6, doi:10.1016/j.sigpro.2006.11.006, pp. 1281--1287, Jun 2007


The DC and Nyquist responses of the filters in a two-channel perfect reconstruction filter bank are expressed in terms of the lifting filters in a lifting decomposition. The computation makes use of the cascade-form representation of lifting steps as lower- and upper-triangular factor matrices in the polyphase-with-advance representation. A functional relationship is derived connecting the DC and Nyquist responses via the polyphase determinant, and it is shown that the responses for a lifted filter bank can be computed recursively using the DC responses of the lifting filters. These results are applied to derive the filter bank normalization specifications in Part 2 of the ISO/IEC JPEG 2000 still image coding standard.

BibTeX Entry

author = {Chris Brislawn and Brendt Wohlberg},
title = {Gain Normalization of Lifted Filter Banks},
year = {2007},
month = Jun,
urlpdf = {http://math.lanl.gov/~brendt/Publications/Docs/brislawn-2007-gain.pdf},
journal = {Signal Processing},
volume = {87},
number = {6},
doi = {10.1016/j.sigpro.2006.11.006},
pages = {1281--1287}