General synthesis procedures for FIR lossless transfer matrices, for perfect-reconstruction multirate filter bank applications

A recently reported procedure for the design of M-channe1 perfect-reconstruction quadrature mirror filter banks uses the concept of “lossless alias-component matrices.” The synthesis of such QMF banks centers around the generation of a lossless M X M FIR transfer matrix E ( z ) . Recent results for such generation have been somewhat ad hoc, Le., not sufficiently general. In this paper, a general procedure is outlined for the generation of such transfer matrices E ( z ) . The procedure is based on a cascaded-lattice structure, derived from a state-space viewpoint. The structure is such that it generates only M X M lossless FIR transfer matrices (regardless of parameter values), and conversely, any M X M lossless FIR transfer matrix can he obtained by a suitable choice of parameters. These parameters turn out to be angles Ok, and the structure is such that the number of angles is minimal. A design example is presented to demonstrate the main results.