In this post, we’ll talk about the trace parameterization of nonnegative Hermitian trigonometric polynomials, providing a proof which depends on the Kalman-Yakubovich-Popov lemma. This follows very closely along the lines of Chapter 2, Section 2.5 of Dumitrescu’s book “Positive Trigonometric Polynomials and Signal Processing Applications” (Springer, 2007).