Adaptive envelope-constrained filtering

In the discrete-time Envelope-Constrained filtering problem, the gain of the filter is minimised subject to the constraint that the filter output to a prescribed input fits into a given envelope. In this paper, a novel adaptive algorithm for solving this problem based on stochastic optimisation is presented. The algorithm is simple to implement on-line and convergence is demonstrated in numerical examples. Under mild regularity assumptions convergence follows from standard stochastic approximation results.