FIR Filter Design via Spectral Factorization and Convex Optimization

We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems with the filter coefficients as the variables and the frequency response bounds as constraints are in general nonconvex. Using a change of variables and spectral factorization we can pose such problems as linear or nonlinear convex optimization problems. As a result we can solve them efficiently (and globally) by recently developed interior-point methods. We describe applications to filter and equalizer design and the related problem of antenna array weight design.