Recursive procedures for constrained optimisation problems and its application in signal processing

Many filter design problems in signal processing can be formulated as a quadratic programming problem with linear inequality constraints. The authors present new recursive procedures for solving this kind of problem. Using a constraint transcription technique, this inequality constrained quadratic programming problem can be approximated as an unconstrained minimisation problem. Two types of optimisation methods are developed to solve this unconstrained problem in a recursive adjusting manner. Analysis and simulation results on the proposed recursive procedures applied to the design of envelope-constrained filters are presented.