GENERAL-SYNTHESIS PROCEDURES FOR FIR LOSSLESS TRANSFER-MATRICES, FOR PERFECT-RECONSTRUCTION MULTIRATE FILTER BANK APPLICATIONS

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