M-channel lifting structure for unimodular filter bank

We extend the method of lifting from M-channel paraunitary filter banks (PUFB) to M-channel unimodular filter banks. In particular, the lifting factorizations of the type I and type II building blocks for the first order unimodular matrices are presented, where the McMillian minimality is preserved. The proposed factorizations continue to have unity diagonal scaling, and perfect reconstruction (PR) is thus guaranteed under finite precision. Using degree-one unimodular building blocks, we present the design of first-order unimodular transforms (a.k.a. lapped unimodular transform, or LUT) and their lifting factorizations. Multiplierless (while reversible) implementations of the resulting LUT are obtained by dyadic approximation of the lifting coefficients.