Additive representations of positive polynomials

The representation of a polynomial which is positive in a finite interval as a sum of two polynomials with specific properties is an important step in the design of recursive digital filters with predetermined phase or delay and Chebyshev stop-band attenuation. It is shown how this problem can be solved taking into account the necessary properties of the polynomial terms in the additive representation. For any positive polynomial a total class of representations can be found. Each representation provides an individual filter realization, and the result of this paper is demonstrated with the aid of an example