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

A recently reported procedure (see ibid., vol.ASSP-35, p.476-492, Apr. 1987 and Proc. IEEE Int. Conf. Acoust., Speech, Sig Processing, Apr. 1987, p.2169-2172) for the design of M-channel perfect-reconstruction quadrature mirror filter (QMF) bands 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 theta /sub k/, and the structure is such that the number of angles is minimal. A design example is presented to demonstrate the main results.