Design of robust envelope-constrained filter with orthonormal bases

In the continuous-time envelope-constrained (EC) filtering problem using al l orthonormal filter structure, the aim is to synthesize an orthonormal fil ter such that the noise enhancement is minimized while the noiseless output response of the filter with respect to a specified input signal stays with in the upper and lower bounds of the envelope. The noiseless output respons e of the optimum Filter to the prescribed input signal touches the output b oundaries at some points. Consequently, any disturbance in the prescribed i nput signal or error in the implementation of the optimal filter will resul t in the output constraints being violated. In this paper, we review a semi -infinite envelope-constrained filtering problem in which the constraint ro bustness margin of the filter is maximized, subject to a specified allowabl e increase in the optimal noisy power gain. 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 c ost, An efficient optimization algorithm is developed based on a combinatio n of the golden section search method and the quasi-Newton method.