Approximation by a Hermitian positive semidefinite Toeplitz matrix

The problem of finding the nearest Hermitian positive semidefinite Toeplitz matrix (in the Frobenius norm) of a given rank to an arbitrary matrix is considered. A special orthogonal basis and equally spaced frequencies allow good initial approximations. A second method using alternating projections solves the case of unrestricted rank. Some interesting numerical results suggest possible applications to signal processing problems.