Chebyshev-polynomial-based Schur algorithm

Presents a new version of the well known Schur algorithm. The Schur algorithm may be used in a wide range of signal-processing applications, from stability tests for discrete time polynomials, through inverse problems and speech coding to the design of orthogonal digital filters. Since the algorithm is iterative in nature there is a tendency for roundoff errors to accumulate through the iterations to the point where the Schur algorithm can become unpractical in certain applications. The design of orthogonal lattice filters is an example of this. The paper expands the polynomials used in the Schur algorithm in terms of Chebyshev polynomials, and reformulates the Schur algorithm in this Chebyshev domain. It is shown that this can lead to smaller roundoff errors than the classical algorithm