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

Using digital orthonormal filters and Lagrangian duality theory, the envelope-constrained (EC) filtering problem has been formulated as a dual quadratic programming (QP) problem with simple constraints. Applying the barrier-gradient and barrier-Newton methods based on the space transformation and gradient flow technique, two efficient design algorithms are constructed for solving this QP problem. An adaptive algorithm, based on the barrier-gradient algorithm, is developed to solve the EC filtering problem in a stochastic environment. The convergence properties are established in the mean and mean square error senses. To demonstrate the effectiveness of the proposed algorithms, a practical example using the Laguerre networks is solved for both the deterministic and stochastic cases.