Envelope-constrained filters: Adaptive algorithms

In this paper we consider an envelope-constrained (EC) optimal filter desig n problem involving a quadratic cost function and a number of linear inequa lity constraints. Using the duality theory and the space transformation fun ction, the optimal solution of the dual problem can be computed by finding the limiting point of an ordinary differential equation given in terms of t he gradient flow An iterative algorithm is developed via discretizing the d ifferential equation. From the primal-dual relationship, the corresponding sequence of approximate solutions to the original EC filtering problem is o btained. Based on these results, an adaptive algorithm is constructed for s olving the stochastic EC filtering problem in which the input signal is cor rupted by an additive random noise, For illustration, a practical example i s solved for both noise-free and noisy cases.