Interior-point methods for magnitude filter design

We describe efficient interior-point methods for the design of FIR filters with constraints on the magnitude spectrum, for example, piecewise-constant upper and lower bounds, and arbitrary phase. Several researchers have observed that problems of this type can be solved via convex optimization and spectral factorization. The associated optimization problems are usually solved via linear programming or, more recently, semidefinite programming. The semidefinite programming approach is more accurate but also more expensive, because it requires the introduction of a large number of auxiliary variables. We propose a more efficient method, based on convex optimization duality, and on interior-point methods for problems with generalized inequalities.