Design of FIR Filters with Discrete Coefficients via Polynomial Programming: Towards the Global Solution

Polynomial programming (PP) deals with a class of optimization problems where both the objective function and constraint functions are multivariable polynomials. PP covers several popular classes of convex optimization problems such as linear, convex quadratic, semidefinite, and second-order cone programming problems, it also includes a good many non-convex problems that are encountered in engineering analysis and design. This paper describes a preliminary attempt to apply a recently developed PP algorithm to the design of FIR digital filters with discrete coefficients. Computer simulations are presented to demonstrate the efficiency of the PP-based algorithm and its ability to provide globally or near-globally optimal designs.