Gradient flow approach to discrete-time envelope-constrained filter designvia orthonormal filters

Using digital orthonormal filters and Lagrangian duality theory, the envelo pe-constrained (EC) filtering problem has been formulated as a dual quadrat ic programming (QP) problem with simple constraints. Applying the barrier-g radient and barrier-Newton methods based on the space transformation and gr adient flow technique, two efficient design algorithms are constructed for solving this QP problem. An adaptive algorithm, based on the barrier-gradie nt algorithm, is developed to solve the EC filtering problem in a stochasti c environment. The convergence properties are established in the mean and m ean square error senses. To demonstrate the effectiveness of the proposed a lgorithms, a practical example using the Laguerre networks is solved for bo th the deterministic and stochastic cases.