Zero location of discrete time linear systems with respect to an orthogonal basis

The problem is considered of a discrete time linear system whose characteristic polynomial is expressed in terms of an arbitrary basis of orthogonal polynomials. It is shown how the Jury-Marden array can be generalised to determine the location of the zeros with respect to the unit circle, without conversion of the polynomial into power form. A generalisation of the Schur-Cohn matrix is also given.