On Parameterizations of First-Order Unimodular Filter Banks

In this paper, two parameterization methods are proposed for M-channel, first-order unimodular filter banks. For such a system with Mcmillan degree of rho, the proposed parameterizations can Q reduce the number of free parameters by rho², compared with existing methods. At the same time, the resulting structures are still complete and minimal in the Mcmillan sense. Besides, perfect reconstruction, unimodular and the filter length constraints can be all structurally imposed. Moreover, the proposed structures offer unconstrained optimizations in the design, which can be hardly achieved by existing methods