A unified approach to structured covariances: Polynomial Vandermonde Bezoutian representations

This paper shows how the theory of recurrence related polynomials is connected to the construction of covariance displacement operators and their diagonalization properties. It is demonstrated that covariance Bezoutians admit a broader class of polynomial Vander-monde based representations, and are not limited to factor circulants, commonly seen in the literature. We show that there is sufficient freedom in the choice of operators, such that more general eigenvector factorizations other than the DFT-based are possible. These become key to achieving efficient matrix-vector multiplications required in signal processing and communications, as the ones arising in modern multicarrier and frequency-domain equalization methods.