Gain normalization of lifted filter banks

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.