Design of robust envelope-constrained filter with orthonormal bases

• Published in: IEEE transactions on signal processing Vol. 48; no. 10; pp. 2881 - 2891
• Main Authors: Chien Hsun Tseng, Kok Lay Tee, Cantoni, A., Zhuquan Zang
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2000; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Applied sciences; Australia; Boundaries; Constraint optimization; Detection, estimation, filtering, equalization, prediction; Disturbances; Exact sciences and technology; Filtering; Filters; Filtration; Information, signal and communications theory; Least squares approximation; Optimization; Optimization algorithms; Permissible error; Radar signal processing; Robustness; Signal and communications theory; Signal design; Signal processing algorithms; Signal, noise; Studies; Telecommunications and information theory; Touch; Filtering; Laguerre function; Signal processing; Robustness; Perturbation; Convex programming; Constrained optimization
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.869041

In the continuous-time envelope-constrained (EC) filtering problem using an orthonormal filter structure, the aim is to synthesize an orthonormal filter such that the noise enhancement is minimized while the noiseless output response of the filter with respect to a specified input signal stays within the upper and lower bounds of the envelope. The noiseless output response of the optimum filter to the prescribed input signal touches the output boundaries at some points. Consequently, any disturbance in the prescribed input signal or error in the implementation of the optimal filter will result in the output constraints being violated. In this paper, we review a semi-infinite envelope-constrained filtering problem in which the constraint robustness margin of the filter is maximized, subject to a specified allowable 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 cost. An efficient optimization algorithm is developed based on a combination of the golden section search method and the quasi-Newton method.