Factorization of high-order linear prediction polynomials

An algorithm for the numerical factorization of very-high-order polynomials with regular root structure is presented. The type of polynomial considered is typical for the z-transform of finite-length signals, with polynomial order N equal to the number of sample points. The algorithm preserves and exploits the stable root structure by solving an associated eigenvalue problem. By application of Lanczos´ algorithm, the computation complexity is constant. Both the method and the algorithm are outlined in detail. Applications include the detection of possibly damped, sinusoidal signals in noise by linear prediction, the numerical evaluation of the complex cepstrum, and phase unwrapping by factorization