A generalization of the Hermite Biehler theorem

The Hermite Biehler theorem gives necessary and sufficient conditions for Hurwitz stability of a polynomial in terms of certain interlacing conditions. In the present paper, the authors generalize the Hermite Biehler theorem to situations where the test polynomial is not necessarily stable, by studying the phase properties of the “frequency response” of a polynomial. Examples are used throughout the paper to complement and illustrate the theoretical development