A Hermitian Toeplitz matrix is unitarily similar to a real Toeplitz-plus-Hankel matrix

Two unitary matrices are presented that transform a Hermitian Toeplitz matrix into a real Toeplitz-plus-Hankel matrix and vice versa. Additional properties and consequences of these unitary transformations are also presented. For a certain class of n-dimensional Toeplitz-plus-Hankel systems of equations, an efficient method of solution is presented. An example is given to illustrate the similarity transforms. Toeplitz-plus-Hankel systems arise in a wide variety of applications, such as linear filtering theory, discrete inverse scattering, and discretization of certain integral equations arising in mathematical physics