A new approach to the weighted peak‐constrained least‐square error FIR digital filter optimal design problem

This paper deals with the design of linear‐phase finite impulse response (FIR) digital filters using weighted peak‐constrained least‐squares (PCLS) optimization. The PCLS error design problem is formulated as a quadratically constrained quadratic semi‐infinite programming problem. An exchange algorithm with a new exchange rule is proposed to solve the problem. The algorithm provides the approximate optimal solution after a finite number of iterations. In particular, the subproblem solved at each iteration is a quadratically constrained quadratic programming. We can rewrite it as a conic optimization problem solvable in polynomial time. For illustration, numerical examples are solved using the proposed algorithm.