 This leads to substantial reduction in the computational complexity, compared to general-purpose semidefinite programming methods that exploit sparsity.A variety of one-dimensional FIR filter design problems can be expressed as convex optimization problems over real trigonometric polynomials, subject to spectral mask constraints.These optimization problems can be formulated as semidefinite programs (SDPs) using classical sum-of-squares (SOS) characterizations of nonnegative polynomials, and solved efficiently via interior-point methods for semidefinite programming.