Design of 2-D Fir Filters Using Positive Trigonometric Polynomials

We propose a method for the minimax design of 2-D FIR filters based on a parameterization of multivariate trigonometric polynomials that are positive on a given frequency domain. The parameterization uses sum-of-squares polynomials and so semidefinite programming (SDP) is applicable. The frequency domain is expressed via the positivity of some trigonometric polynomials. The degree of sum-of-square polynomials must be bounded and so the method is in principle suboptimal, but the 2-D FIR filter designs we study numerically suggest that near-optimal results are obtained