  Matrix-valued covariance extension and multivariate spectral estimation are
formulated as generalized moment problems in the "THREE" approach and its
extensions. Under this context, we discuss Theorem 6 in \cite{Georgiou-06}
concerning the bijectivity of a moment map defined over a parametric family of
spectral densities. In particular, we provide a counterexample in which the
moment map under consideration is shown to have a critical point, namely a
point at which the Jacobian loses rank. Then with standard techniques in
bifurcation theory, we conclude further that the computed critical point is a
bifurcation point, which means that the moment map is not injective.
