Unitary Hessenberg and state-space model based methods for the harmonic retrieval problem

The connections between two families of methods for the harmonic retrieval problem are explored: the unitary Hessenberg methods and the state-space model based methods. It is shown that in a noise-free situation, the unitary Hessenberg methods can be understood as one particular case of a very popular high resolution algorithm, the Toeplitz approximation method (TAM) of S.Y. Kung (1981)