1. FIR Filter Design via Spectral Factorization and Convex Optimization 1 FIR Filter Design via Spectral Factorization and Convex Optimization

We consider the design of nite impulse response (FIR) lters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the lter coe cients 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 e ciently (and globally) by recently developed interior-point methods. We describe applications to lter and equalizer design, and the related problem of antenna array weight design. To appear as Chapter 1 of Applied Computational Control, Signal and Communications, Biswa Datta editor, Birkhauser, 1997. The paper is also available at URL http://www-isl.stanford.edu/people/boyd and from anonymous FTP to isl.stanford.edu in pub/boyd/reports. 2 Shao-Po Wu, Stephen Boyd, Lieven Vandenberghe