Bounded Real Lemma for multivariate trigonometric matrix polynomials and FIR filter design applications

We propose a linear matrix inequality formulation of the Bounded Real Lemma (BRL) for multivariate trigonometric polynomials with matrix coefficients. This is a generalization of previous results regarding positive trigonometric polynomials. The proposed BRL allows the formulation of several FIR filter design problems as semidefinite programming (SDP) problems. We employ the new BRL in three applications: matrix filter design, 2-D deconvolution and design of 2-D filters with matrix coefficients. All applications are illustrated with examples that improve on previous work.