Algebraic approach to discrete-time polynomial spectral factorization

In this paper we propose an algebraic approach to the discrete-time polynomial spectral factorization problem, which has a significant importance in signal processing and control for finite dimensional linear systems. We also attempt to generalize the approach and establish a new frame-work of symbolic optimization of algebraic functions that is relevant to possibly a wide variety of practical application areas. The crucial aspects of the framework are the suitable use of algebraic methods coupled with the discovery and exploitation of structural properties of the problem in the conversion process into the framework, and the feasibility of algebraic methods when performing the optimization. Two examples are also included to demonstrate the significance and relevance of the proposed approach and framework