FIR filter optimization with POS3POLY in CVX

POS3POLY is a new library for solving convex optimization problems with positive polynomials, designed and written by the current authors. POS3POLY allows simple descriptions of three types of positive multivariate polynomials, namely trigonometric, real and hybrid, sparing the user of the task of parameterizing them with linear matrix inequalities. Positivity on semialgebraic domains and a polynomial Bounded Real Lemma are also treated. In this paper, we present the features of POS3POLY that allow the manipulation of positive trigonometric polynomials in CVX and are useful in FIR filter optimization. Three fully detailed examples are given, for designing peak-constrained least-squares linear-phase filters, sparse 2D linear-phase filters and 2D approximately linear-phase filters.