Design of nonlinear phase FIR digital filters using quadratic programming

This paper presents two methods for the design of FIR filters with arbitrary magnitude and phase responses according to a weighted mean squared error criterion with constraints on the resulting magnitude and phase errors. This constrained least square criterion allows for an arbitrary trade-off between pure L₂ filters and Chebyshev filters. The resulting nonlinear optimization problem is either converted into a standard quadratic programming problem (method 1) or exactly solved by a sequence of quadratic programs (method 2). The quadratic programming problems can be solved efficiently using standard software