Robust envelope-constrained filter design with Laguerre bases

The envelope-constrained filtering problem is concerned with the design of a filter such that the noise enhancement is minimized while the noiseless filter response stays within an envelope. Naturally, the optimum filter response to the prescribed input signal tends to touch the output boundaries at some points. Consequently, any disturbance to the prescribed input signal could result in the output constraints being violated. In this paper, we formulate a semi-infinite constrained optimization problem in which the margin of the constraint robustness of the filter is maximized. Using a smoothing technique, it is shown that the solution of the optimization problem can be obtained by solving a sequence of strictly convex optimization problems with integral cost.