Lifted linear phase filter banks and the polyphase-with-advance representation [JPEG 2000 image coding applications]

We develop the noncausal polyphase-with-advance representation that underlies the theory of lifted filter banks and wavelet transforms used in the ISO/IEC JPEG 2000 image coding standard. The theory includes a matrix algebra framework for analyzing linear phase two-channel filter banks. Whole- and half-sample symmetric filter banks are characterized completely in terms of the theory, and linear phase lifting factorizations are developed for both classes of linear phase filter banks.